unit 8 reflection of light in mirrors

Unit 8

Reflection of Light in Mirrors

Table of Contents

Table of Contents 1

Introduction 3

Essential Questions 4

Review 4

Lesson 8.1: Reflection of Light 5 Objectives 5 Warm-Up 5 Learn about It 6 Key Points 9 Web Links 10 Check Your Understanding 10 Challenge Yourself 11

Lesson 8.2: Convex Mirrors 12 Objectives 12 Warm-Up 12 Learn about It 13 Worked Examples 16 Key Points 22 Web Links 22 Check Your Understanding 22 Challenge Yourself 24

Lesson 8.3: Mirror Equation 25 Objectives 25 Warm-Up 25 Learn about It 26 Worked Examples 28 Worked Examples 31 Key Points 34

Web Links 34 Check Your Understanding 34 Challenge Yourself 35

Lesson 8.4: Concave Mirrors 36 Objectives 36 Warm-Up 36 Learn about It 37 Worked Examples 41 Key Points 47 Web Links 47 Check Your Understanding 47

Laboratory Activity 49

Performance Task 50

Self Check 51

Key Words 52

Key Formula 53

Wrap Up 54

Photo Credits 55

References 55

Answer Key 56

Copyright © 2018 Quipper Limited 2

GRADE 10 | SCIENCE

Unit 8 Reflection of Light in Mirrors

Mirrors are used in different applications. It is used in several laboratory equipments and apparatus for its ability to form various characteristics of images that enhances the object for observation. Perhaps one of the most life-saving uses of mirrors is its utilization in automobiles. Side mirrors and rear view mirror in cars serve as precautionary factors when deciding to turn, speed up, slow down, and when parking. These mirrors are convex mirrors which produce a wider view of the images at the back of the car. This type of mirror makes objects appear smaller, hence, the sign on new car mirrors “Objects in mirror are closer than they appear.” With various uses of mirrors, it is inevitable for one to wonder how mirrors create images. This unit will discuss the reflection property of light and its behavior when striking mirrors.


Essential Questions

At the end of this unit, you should be able to answer the following questions.

● How does light behave when striking mirrors? ● How do mirrors create images? ● What are the types of mirrors and what makes one different from the other? ● How can one predict the type, orientation, and position of an images formed

from different types of mirrors using ray diagram techniques? ● How can one predict the type, orientation, and position of an images formed

from different types of mirrors using mirror equation?

Review

● Electromagnetic waves are waves that are made of electric and magnetic field components. They do not need a medium to propagate, hence, they can travel through space.

● Among the different types of electromagnetic waves, only visible light has its own spectrum, and is visible to the human eye.

● Light travels in a straight line in a vacuum, and has both wave-like and particle-like nature.

● Light, as well as EM waves, exhibits different behaviors when it encounters a medium. Some of the behaviors of light were reflection, refraction, dispersion, absorption, interference, diffraction, transmission, and scattering.

● Reflection is the bouncing of light when it reaches the boundary between two media; light stays in the original medium.

● Refraction is the bending of light as it passes from one medium to the other. ● Magnification is a unitless value that tells how much something is enlarged. ● Orientation tells whether the image is upright or inverted.


Lesson 8.1: Reflection of Light

Objectives In this lesson, you should be able to:

● discuss the reflection of light and law of reflection in mirrors; ● differentiate diffuse and specular reflection; and ● predict the type, orientation, and position of an image formed by

plane mirrors.

Light travels in a straight line, specifically in a vacuum. It has several properties and is influenced usually by the medium where it propagates. One property of light is it bounces off as it strikes a surface, what particular property of light enables it to bounce off a surface?

Warm-Up

AirPLANE mirrors Materials:

● plane mirror (at least 1’ ✕ 1’ size) ● toy airplane (or a printed photo of an airplane)

Procedure:

1. Observe the toy airplane in terms of its height, width, and other physical appearance. You may use a ruler to measure or as reference.

2. Place the toy airplane in front of the plane mirror. 3. Observe the image of the toy airplane from the mirror.

Guide Questions:

1. What similarities and differences did you notice from the object (actual toy) and the image (shown in the mirror)?

2. Are the height and width of the image and object the same? Why or why not? 3. Is the image vertically upright or not relative to the object? Why or why not?


Learn about It

Behavior of Light and Law of Reflection Light ordinarily travels in straight line path called ray. This means that in order for light to go from one point to another, it takes the shortest and most efficient path available to it. The idea that the path which light travels is the one that uses the shortest time is called Fermat’s principle of least time, formulated by the French scientist Pierre Fermat in 1650.

Fig. 1. Light takes the shortest path possible.

If light needs to strike a medium in order to get from one point to another, the photon must strike the surface in such a way that the travel time between the two points will be the least. The study dealing with the path of light as it strikes a medium which involves straight-line rays at various angles is referred to as geometric optics.

Fig. 2. The path light takes when striking a reflective surface.

The angle of incidence, 𝜃i ,is the angle which an incident ray makes with an imaginary line perpendicular to the surface, referred to as the normal. The angle of reflection, 𝜃 r , is the angle which the reflected ray makes with the normal.


The law of reflection states that the incident and reflected rays lie in the same plane with the normal and that the angle of reflection equals the angle of incidence, 𝜃 i = 𝜃 r.

Fig. 3. The law of reflection which states that the angle of incidence is always equal

to the angle of reflection.

Diffuse and Specular Reflection Diffuse reflection happens when light is reflected into multiple directions. This happens when light hits a rough surface. Objects that might appear smooth to touch but still performs diffuse reflection are actually microscopically rough. One good example is an eggshell. An eggshell can be smooth to touch but microscopically has small bumps causing light to be diffused in many different directions. Ordinary objects can be viewed at many different angles since light is reflected by the object in many directions.

Fig. 4. Diffuse reflection on a rough surface which shows light rays reflected in

multiple directions.


When a beam of light hits a mirror, light will not hit your eyes unless your eye is positioned at the right place where the law of reflection is satisfied. Since mirrors are microscopically smooth, light rays travel at only one path. This kind of reflection is called specular reflection (speculum is Latin for mirror).

Fig. 5. Diffuse reflection (a) vs. specular reflection (b).

When someone looks on a mirror, it would appear that the objects (or even the observer) are located beyond the mirror even though they are not. The one seen beyond the mirror is called image, while the one that produces the image is the object. Simply speaking, objects are the source of incident light. Plane Mirror A plane mirror is a smooth, flat reflecting surface. It creates images that are located on the same distance as the object from the mirror and with the same height but are inverted from left to right.

Fig. 6. Image formation by a plane mirror.


The law of reflection is followed when images are formed by mirrors. The image appears to be formed as far behind as the object in front. The image distance, di, which is measured from image location to mirror, is equal to the object distance, do, which is measured from object location to mirror. The images formed by plane mirrors are virtual images. Light rays do not actually pass through the image location itself; it just appears to be. There are no actual rays converging behind the mirror (thus, virtual) which makes it impossible to project the image on any surface placed at the location of image. Real images are the opposite of virtual images and can be projected on surface placed at the image position. This is due to the fact that actual rays converge to a point forming a ‘real’ image.

Key Points

● Light travels in straight line paths called rays, and travels a path which uses the shortest time which is an idea of Fermat’s principle of least time.

● The law of reflection states that the incident and reflected rays lie in the same plane with the normal and that the angle of reflection equals the angle of incidence.

● Diffuse reflection happens when light is reflected into multiple directions, while specular reflection happens when a light hits a microscopically smooth mirror.

● A plane mirror is a smooth, flat reflecting surface. Images formed by this mirror are virtual images.


Web Links

For further information about reflection of light, you can check the following web links:

● Read this article to understand more about the law of reflection and if a diffuse reflection obeys this lay microscopically. Davidson, Michael W. & The Florida State University. 2018. ‘Specular and Diffuse Reflection.’ http://micro.magnet.fsu.edu/primer/java/reflection/specular/

● Watch this video to know how mirrors are created using glass and silver nitrate. Tech Insider. 2017. ‘Watch This Artist Create A Mirror Using Glass And Silver Nitrate.’ https://www.youtube.com/watch?v=atCtLsh4MBs

Check Your Understanding

A. Read and analyze the following statements given. Identify what is being described by each of the given statements. 1. It is the type of reflection that happens when light is reflected into

multiple directions. 2. It is study dealing with the path of light as it strikes a medium which

involves straight-line rays at various angles. 3. It is the idea or principle that tells that the path which light travels is the

one that uses the shortest time. 4. It is the type of reflection that happens when light hits a microscopically

smooth surface. 5. It is the opposite of virtual images. 6. It is the angle which an incident ray makes with an imaginary line

perpendicular to the surface. 7. It is the law that states that the angle of reflection is always equal to the

angle of incidence. 8. It is the angle which the reflected ray makes with the normal. 9. It is a smooth, flat reflecting surface.

10. It is the type of images formed by plane mirrors.


http://micro.magnet.fsu.edu/primer/java/reflection/specular/

https://www.youtube.com/watch?v=atCtLsh4MBs

B. Identify whether each situation uses diffuse or specular reflection. Write D if it is diffuse reflection, otherwise write S. 1. You see a clear reflection of your body in a plane mirror. 2. A fisherman sees a reflection of the sky on the rough waters of a lake. 3. Light is shined on a concrete floor. 4. A car sees a wide view of the road behind it through the side mirrors. 5. You pointed a flashlight on a shiny black wall.

Challenge Yourself

Answer the following questions. 1. Why can’t you see your reflection in the mirror if the room is very dark? 2. Will there be any possibility that you can have a magnified image using a

plane mirror? Why? 3. Why can’t you see a clear and distinctive image of yourself in a plane

concrete floor? 4. How can the position of the image be determined when using a plane

mirror? 5. Are mirrors used for driving vehicles plane mirrors? What type of mirror is

this? What is its difference from plane mirrors?


Lesson 8.2: Convex Mirrors


● identify the parts of a curved mirror; ● differentiate plane, convex and concave mirrors as well as the

images that they form; and ● apply ray diagramming techniques in describing the

characteristics and positions of images formed by mirrors.

Convex mirror is a type of mirror usually used by automobiles and convenience stores. They are useful in seeing a wide-angled view of a portion of a driveway or of a store. What makes convex mirrors useful in these kind of situations?

Warm-Up

Spoon-tastic mirror! Materials:

● spoon ● small toy or a colored push pin

Procedure:

1. Observe the toy in terms of its height, width, and other physical appearance. You may use a ruler to measure or as reference.

2. Place the toy in front of the back of the spoon as a mirror. 3. Observe the image (shown in the mirror) formed from the actual toy.

Guide Questions:




Learn about It

Parts of a Curved Mirror Diagram Curved mirrors are mirrors that form a section of a sphere. This curve has numerous parts. The principal axis is an imaginary line passing through the center of the sphere at the exact center of the mirror. The point on the mirror’s surface where the principal axis meets the mirror is known as the vertex. The point in the center of the sphere from which the mirror was sliced is known as the center of curvature, C. Halfway between the center of curvature and vertex is the focal point, F. The distance between the vertex and the focal point is the focal length, f.

Fig. 7. The different parts of a curved mirror diagram.

There are two types of curved mirrors—convex and concave mirrors. A convex mirror is a curved mirror wherein the reflecting surface is on the outer surface of the sphere so that the center of the mirror bulges towards the viewer. This mirror focuses light away from the focal point that is why it is called diverging mirror.

Fig. 8. The back of a spoon acts a convex mirror for the pushpin.


Ray Diagramming Techniques for Convex Mirrors In order to find where an image will be located if an object is placed in front of a mirror, a technique called ray diagramming is used. It uses three reference rays in order to locate the image. Object in ray diagrams are usually represented by bold and thick arrows. In the illustration below, an object is represented by an orange arrow. First, a reference ray starting from the object going parallel to principal axis is drawn. It reflects through the focal point, F, after it hits the mirror. This is called the principal ray.

Fig. 9. Drawing the principal ray for a convex mirror.

The second reference ray goes through F and then goes parallel to principal axis after hitting the mirror. This is called the focal ray.

Fig. 10. Drawing the focal ray for a convex mirror.


The third reference ray goes through C then goes back along itself through C. This is called the central ray.

Fig. 11. Drawing the central ray for a convex mirror.

Since the F and C of a convex mirror are situated behind the mirror’s surface, dotted lines are extended along the reflected rays to points behind the mirror. The intersection of two or more rays locates the image.

Fig. 12. Ray-diagramming for a convex mirror.

The created images in convex mirrors are always located behind the mirror – virtual, upright and diminished (smaller than the object). Because of these characteristics, the images formed by convex mirrors are easily predictable.


Worked Examples

Example 1 Determine the location and characteristics of the image of the arrow using ray diagramming techniques in the given illustration below.

Solution: Step 1 Draw the principal ray.


Step 2 Draw the focal ray.

Step 3 Draw the central ray.

Step 4 Draw the image formed on the intersection of lines.

Therefore, the image which is upright, virtual and reduced is formed at the back of the mirror.


Let us Practice Given the illustration below, determine the location and characteristics of the image of the arrow using ray diagramming techniques.

Example 2 What is the orientation, size, and type of image formed from the object positioned in front of a convex mirror below?





Step 4 Draw the image on the intersection of lines.

The image is formed at the back of the mirror. It appears upright, diminished (smaller) and it is a virtual image.


Let us Practice What is the orientation, size and type of image formed from the diagram below?

Example 3 What is the orientation, size, and type of image formed from the object positioned in front of a convex mirror if the object’s distance from the mirror is 40 cm? Solution: Step 1 Draw the diagram for the situation.

Step 2 Draw the principal ray.





The image is formed at the back of the mirror. It appears upright, diminished (smaller) and it is a virtual image.

Let us Practice An object was placed in front of a diverging mirror which has a focal length of 0.5 m. If object’s distance was 1 meter from the mirror, what is the orientation, size and type of the image formed?


Key Points

● A convex mirror is a curved mirror wherein the reflecting surface is on the outer surface of the sphere so that the center of the mirror bulges towards the viewer.

● Ray diagramming techniques involves the drawing of the principal ray, focal ray, and the central ray.

● The created images in convex mirrors are always located behind the mirror – virtual, upright and diminished (smaller than the object).

Web Links

For further information on convex mirrors, you can check the following web links:

● Read this article to know more about the different uses of convex mirrors. Specadel Technologies PRivate Limited. n.d.. ‘10 Uses Of Convex Mirrors.’ http://www.edurite.com/kbase/10-uses-of-convex-mirror

● Watch this video to understand more about the proper way to draw and illustrate ray diagram using pen and ruler. Mr. Primmer’s VIDEOS!!!. 2016. ‘Ray Diagrams for Convex Mirrors.’ https://www.youtube.com/watch?v=NJ5EQE47IyM


A. Read and analyze the following statements given. Write T if the statement is correct, and F if it is false. 1. There are usually three rays in ray diagramming for convex mirrors. 2. Ray diagramming techniques follows the law of reflection 3. In ray diagramming of mirrors, it is assumed that no refraction will occur. 4. Curved mirrors are mirrors that form a section of a sphere. 5. Convex and concave mirrors form the same characteristics of images.


http://www.edurite.com/kbase/10-uses-of-convex-mirror

https://www.youtube.com/watch?v=NJ5EQE47IyM

B. Match column B with its definition in column A. Write the letter of your answer on the space before each number.

Column A Column B

1. It is the point that is halfway between the center of curvature and vertex.

2. It refers to a point in the center of the

sphere from which the mirror was sliced.

3. This is also known as a diverging mirror.

4. It is an imaginary line passing through the center of the sphere at the exact center of the mirror.

5. It is a point on the mirror’s surface

where the principal axis meets the mirror.

6. A type of curved mirror wherein the

reflecting surface is on the outer surface of the sphere so that the center of the mirror bulges towards the viewer.

7. It is a technique that uses three

reference rays in order to locate the image.

8. It also means that the image is smaller

than the object.

9. It is used to describe an image formed behind the mirror.

10. A type of mirror that focuses light away

from the focal point

a. diminished b. magnified c. virtual d. upright e. vertex f. center of curvature g. convex mirror h. concave mirror i. principal axis j. focal point k. ray diagramming


Challenge Yourself

1. Is there any possibility that a convex mirror will produce a magnified image? Why?

2. What are the other uses of the convex mirror? 3. Is it possible to determine the characteristics of the image formed using the

convex mirror without ray diagramming? How? 4. In which region will the image appear using the following diagram below? 5. What are the characteristics of the image formed in the diagram below?


Lesson 8.3: Mirror Equation


● predict the type, orientation, and position of an image formed by different kinds of mirrors using the mirror equation and the ray diagram method; and

● compute for the magnification of an image.

Ray diagramming only presents the image qualitatively. Manufacturing mirrors, especially those which has critical uses such as side mirrors in automobile, requires accurate measurement of a part of a mirror such as the focus. So, it is important to know the precise characteristics of the images formed. How to predict the characteristics of the image formed by mirrors without ray diagrams?

Warm-Up

Would you like it plane or curved?

Materials: ● plane mirror ● spoon ● two identical small toy or colored push pin

Procedure:

1. Position a toy in front of the plane mirror and another toy in front of the back of the spoon. Make sure that the toys are equidistant from the mirrors.

2. Observe the images formed from the two mirrors. Guide Questions:

1. In which mirror is the image formed larger? 2. What causes this difference in size of images formed? 3. What would be the size of the image if the other side of the spoon was used?


Learn about It

Mirror Equation It is possible to not have all the rays meet when using ray diagrams. Ideally, all three rays should meet but most of the time, only two rays would. This is mostly due to human error when doing ray diagrams. There is only one condition when an image will not be formed when placed in front of a mirror.

Fig. 14. All rays produced from any reference point of an object will converge if they

should converge. It is possible to mathematically calculate where an image will show up if distance of the object is known. It is also possible to know the radius of curvature of a mirror given the location of object and the image. The object distance, image distance and the radius of curvature are interdependent. The equation that relates the three is called the mirror equation. A set of sign conventions for the three variables must be established for use with the mirror equation.

p is the object distance, q is the image distance and f is the focal length of the image. Units for distances and focal length should be consistent.Take note of the sign conventions shown in Table 1 for the mirror equation.


Table 1. Sign conventions for the mirror equation.

Symbol Situation Sign Illustration

p object is in front of the mirror

+

q image is in front of the mirror (real image)

+

q image is behind the mirror (virtual image)

-

R, f center of curvature is in front of the mirror (concave mirror)

+

R, f center of curvature is behind the mirror (convex mirror)

-

R, f mirror has no curvature

∞


Worked Examples

Example 1 What is the focal point distance of a convex mirror if the object located 10 cm away from the mirror forms a virtual image which is 30 cm away from the mirror? Solution Step 1 Identify what is required to find in the problem. You are asked to find for the focal point distance (f). Step 2 Identify the given in the problem. The object distance and image distance are given. p = 10 cm and q = (-30 cm) Step 3 Write the working equation.

Step 4 Substitute the given values.

Step 5 Find the answer.

Therefore, the focal point distance is 15 cm.

Let us Practice An image was formed 0.5 m away from the mirror, which is unclassified. The object was placed 0.5 m away from the mirror. What is the focal distance of the mirror? What type of mirror is it?


Example 2 An object was placed 1m away from the mirror. If it has a focal length of 1.2 m, how far will the image formed be from the convex mirror? Where will the image form? Solution: Step 1 Identify what is required to find in the problem.

You are asked to image distance (q). Step 2 Identify the given in the problem.

The object distance and the focal length are given. p = 1 m and f = (-1.2 m) Step 3 Write the working equation.



Therefore, the image distance is 0.55 m away from the mirror. The image is formed behind the mirror because of the negative sign.

Let us Practice Where will the image of an object 5 meters away from the convex mirror with 2.5 m focal length form? How far is it from the mirror?


Example 3 A concave mirror is is a curved mirror wherein the reflecting surface is on the inner surface of the sphere so that the center of the mirror sinks away from the viewer. A concave mirror with a center of curvature of 40 cm, produced an image that is 35 cm in front of a mirror. How far is the object placed? Solution Step 1 Identify what is required to find in the problem. You are asked to find for the object distance (p). Step 2 Identify the given in the problem. The center of curvature (C) and image distance (q) are given. C = 40 cm and q = 35 cm Step 3 Write the working equation.



Therefore, the object was placed 46.67 cm away from the front of the mirror.

Let us Practice A convex mirror has a center of curvature of 2 m. An object was placed 1.25 m away from this mirror. How far and where will the image appear?


Magnification of Image The magnification of an image formed by mirrors can be computed either by using the height of the image and the object or their distances. A positive M means that image is upright and virtual and a negative value means it is inverted and real.

The image height is denoted by h’, while the object distance is h. For distances, the denotation is similar to that of the mirror equation: q for the image distance, and p for the object distance. Units of the height and distances should be consistent.

Worked Examples

Example 1 What is the magnification of a convex mirror if it produced a 43 cm high image from a 55 cm high object? Solution Step 1 Identify what is required to find in the problem. You are asked to find for the magnification (M). Step 2 Identify the given in the problem. The image height and object height are given. h’ = 43 cm and h = 55 cm Step 3 Write the working equation.



Step 5 Find the answer. Therefore, the magnification of the convex mirror is 0.78.

Let us Practice What is the magnification of a mirror which produced an image which has the same height as the object at any distance? What type of mirror is it?

Example 2 A mirror has a magnification of 2.5 times. How far will the image be formed from the mirror if the object is placed 0.5 m away from the mirror? Solution: Step 1 Identify what is required to find in the problem.

You are asked to find the image distance. Step 2 Identify the given in the problem.

The magnification and object distance are given. M = 2.5 and p = 0.5 m Step 3 Write the working equation.



Therefore, the image distance is 1.25 m. the image will form in front of the mirror.


Let us Practice How far is the object placed in front of a 2.0 times magnifying mirror when the image was shown 30 cm in front of the mirror?

Example 3 A 70 mm wide rubix cube was magnified to a 92 mm wide cube (image). How far is the object when the image was formed 30 cm from the mirror? Solution Step 1 Identify what is required to find in the problem. You are asked to find object distance. Step 2 Identify the given in the problem.

The object and image height (the width of a cube is equal to its height), and image distance are given. h = 70 mm, h’ = 92 mm, and q = 30 cm

Step 3 Write the working equation.


Step 5 Find the answer. Therefore, the object distance is 22.83 cm.

Let us Practice Dave has a height of 175 cm. If he is 0.5 m away from the front of a magnifying mirror, his height is increased by 10 cm. How far from the mirror is his image?


Key Points

● Mirror equation relates the object distance, image distance and radius of curvature. It is given by the formula:

● Magnification can be computed either by using the height of the image and

the object or their distances. It is given by the formula:

Web Links

For further information on mirror equation, you can check the following web links:

● Read the mirror equation in concave mirrors. The Physics Classroom.. ‘The Mirror Equation - Concave Mirrors.’ http://www.physicsclassroom.com/class/refln/Lesson-3/The-Mirror-Equation

● Watch an animation of the explanation of the mirror formula and magnification. 7activestudio. 2015. ‘MIRROR FORMULA AND MAGNIFICATION.’ https://www.youtube.com/watch?v=cQ492W3VSfc


A. Identify the relationship of the following. Indicate it as directly proportional if one of the quantity increases or decreases after the other increases or decreases at the same time, otherwise, indicate it as inversely proportional. 1. magnification and image height 2. magnification and image distance 3. magnification and object distance


http://atomictimeline.net/

https://www.youtube.com/watch?v=drCg4ruJCfA

4. image height and image distance 5. object height and image distance

B. Identify whether the image will be magnified, diminished or undiminished

(same size as the object). Write M, D, or U, respectively. 1. A mirror has a magnification power of 0.75. 2. A mirror has a magnification power of 1. 3. A mirror has a magnification power of 2.25. 4. An object which is 35 cm high appears to be 20 cm in front of a mirror. 5. A toy car in front of a plane mirror.

C. Solve the following problems.

1. What is the magnification power of a mirror which increases a ballpens’ height (9 cm) by 2 cm?

2. How far will an object appear (image distance) if it is placed 1 meter away from a convex mirror with focal length of 40 cm?

3. How far will an object appear (image distance) if it is placed 1 meter away from a concave mirror with focal length of 40 cm?

4. How far will an object appear (image distance) if it is placed 1 meter away from a plane mirror?

5. What should be the object’s distance if its image should appear 30 cm behind a convex mirror with a focal length of 45 cm?

Challenge Yourself

Answer the following questions. 1. Why do plane mirrors form images with the distance similar to that of the

object? 2. If the object is placed at an infinite distance, will the image still appear in a

convex lens? 3. If the object is placed at an infinite distance, will the image still appear in a

concave lens? 4. If the object is placed at an infinite distance from a plane mirror, what will be

its image distance? 5. Is it possible for a concave mirror to produce an image with a similar size to

that of an object? How?


Lesson 8.4: Concave Mirrors


● differentiate plane, convex and concave mirrors as well as the images that they form; and

● apply ray diagramming techniques in describing the characteristics and positions of images formed by mirrors.

Convex mirror is indeed very helpful in creating diminished image which makes it ideal for automobiles and convenience stores usage. However, there are certain jobs that needs magnification of reflections such as that in the cosmetics and dentistry industries. What type of mirror produces an enlarged real image?

Warm-Up

Spoon-tastic (reversed) Mirror Materials:

● spoon ● small toy or a colored push pin

Procedure:

1. Observe the toy in terms of its height, width, and other physical appearance. You may use a ruler to measure or as reference.

2. Place the toy in front of the other curved side of the spoon as a mirror. 3. Observe the image (shown in the mirror) formed from the actual toy.

Guide Questions:




Learn about It

Concave Mirrors A concave mirror is a curved mirror wherein the reflecting surface is on the inner surface of the sphere so that the center of the mirror sinks away from the viewer.

Fig. 15. The front of a spoon acts as a concave mirror for the pushpin.

It is also called a converging mirror because it focuses light rays towards its focal point. It can produce both real and virtual images depending on where the object is placed in front of it. Ray Diagramming Techniques for Concave Mirrors The figure below shows how a concave mirror forms an image (h is the object’s height, h’ is the image height, p is the object’s distance from the mirror and q is the image’s distance from the mirror).

Fig. 13. Ray diagrams showing the image formation by a concave mirror.


When an object is placed in front of a concave mirror, light rays extend from the object towards the mirror.The light rays that hit the mirror are then focused towards the center of the curvature. The meeting of light rays forms the image. If the image formed by the concave mirror is real, it can be projected on a screen or on a film placed at the location of the image. To draw the ray diagram for a concave mirror, the principal ray is drawn. It is parallel to the principal axis and will be reflected to the focal point.

Fig. 17. Drawing the principal ray for concave mirrors.

Next, the focal ray is drawn. It passes through the focal point and is reflected parallel to the principal axis.

Fig. 18. Drawing the focal ray for concave mirrors.


The central ray was drawn next. It passes through the central point and will be reflected back to the central point.

Fig. 19. Drawing the central ray for concave mirrors

The point where the rays intersect is where the image will appear.

Fig. 20. Image formation by concave mirrors.

A concave mirror can form different kinds of images depending on where objects are located in relation to the center of curvature and focal point.


Fig. 17. The characteristics of the images formed by concave mirrors for different object positions.


Worked Examples

Example 1 Determine where the image will appear when an object is placed in front of a concave mirror. Use ray diagramming techniques on the figure below.






Therefore, the image is formed in between the center of curvature and focal point. It is an inverted, diminished and real image.


Let us Practice An object was placed at an infinite distance in front of a concave mirror. Determine the characteristics and location of the image formed through ray diagramming.

Example 2 An object was placed between the center of curvature and focus of a concave mirror as shown in the illustration below. Determine the location and the characteristics of the image formed using ray diagrams.






The image is formed beyond the center of curvature. It appears inverted, magnified and it is a real image.


Let us Practice An object is placed on the center of curvature of a concave mirror. Draw the ray diagram of image formation to determine the location and characteristics of the image formed.

Example 3 An object is located 15 cm away from a converging mirror which has a 1-meter center of curvature. What would be the location and characteristics of the image formed? Solution: Step 1 Draw the principal ray.





The image is formed in between the focal point and the mirror. It is an upright, magnified and virtual image.

Let us Practice A 5 feet tall person stands 12 cm away from a concave mirror which has a focal length of 8 cm. What would be the location and characteristics of the image formed in this scenario?


Key Points

● A concave mirror is a curved mirror wherein the reflecting surface is on the inner surface of the sphere.

● Ray diagramming techniques involves the drawing of the principal ray, focal ray, and the central ray.

● The created images in concave mirrors depends on the distance of the object from the mirror.

Web Links

For further information on concave mirrors, you can check the following web links:

● Read this article to know more about the different uses of concave mirrors. Aenne, Rachel. 2018. ‘Simple Uses of Concave Mirrors.’ https://sciencing.com/simple-uses-concave-mirrors-7298957.html

● Watch this video to understand more about a mirascope, an optical device creates a real 3D image. Uploaded by user derinsherman62t. 2013. ‘How the Mirage/Mirascope creates a real 3D image.’ https://www.youtube.com/watch?v=33IvhNsiPb4


A. Complete the anagram below. 1. concave: converge :: convex: __________ 2. inner surface of sphere: diverging mirror :: outer surface of sphere:

__________ 3. real: in front of mirror :: virtual: __________ 4. real: virtual :: upright: __________ 5. real: virtual :: magnified: __________


http://atomictimeline.net/

https://www.youtube.com/watch?v=33IvhNsiPb4

B. Modify the underlined term(s) to make the statement correct. Otherwise, write true. 1. A concave mirror is also called a diverging mirror. 2. A convex mirror can produce both real and virtual images. 3. In a concave mirror, the position of an object is crucial to the

characteristics of the formed image. 4. The meeting of light rays forms the image. 5. If the image formed by the concave mirror is real, it can be projected on a

screen or on a film placed at the location of the image. 6. In a concave mirror, if the object is at an infinite length away from the

mirror then it will appear on the focal point. 7. If an object is placed on the center of curvature of a concave mirror, the

image will be undiminished in size. 8. If the object is placed within the focal length of a concave mirror, its image

magnification is greater than 1. 9. If the object is placed between the focal length and center of curvature of

a concave mirror, then the image formed will be inverted. 10.If the object is placed between the focal length and center of curvature of

a concave mirror, then the image formed will be a real image.

Answer the following questions.

1. How does a mirascope, an optical device which creates a hologram, work? 2. Why is converging lens used in dentistry rather than a diverging lens? 3. Is using converging lens in driving useful? How? 4. What are the other uses of concave mirrors? 5. Which type of mirror is used in microscopes? Why is this so?


Laboratory Activity

Activity 8.1 Law of Reflection

Objectives At the end of this laboratory activity, the students should be able to:

● verify the law of reflection by measuring the angles of incidence and reflection; and

● discuss the reflection of light and law of reflection in mirrors. Materials and Equipment

● plane mirror ● laser(s) ● protractor

Procedure

1. Position the laser such that it hits the mirror at an angle of 20° with the normal line (line perpendicular to the point where the light hits the plane mirror and the mirror itself).

2. Record the measurement of the angle of reflected light with respect to the normal line in table 1. Repeat this for three trials.

3. Repeat the steps with laser angles’ 30°, 40°, and 50°. Data and Results Table 1. Angle of reflection measured given the angle of incidence.

Angle of Incidence, degrees

Angle of Reflection, degrees

Trial 1 Trial 2 Trial 3 Average

20

30

40

50


Guide Questions 1. What can you notice on the relationship of the angle of incidence and angle

of reflection using the plane mirror? 2. Does your angle measurements in each trial follow the law of reflection? Why

or why not? 3. If you are to continue measuring the angle of reflection of a laser incident at

75 degrees, what will be the outcome? 4. Will the law of reflection still, hold true for convex and concave mirrors? 5. Are your angle measurements exactly equal with each other? What could be

the causes of error in measuring?

Performance Task

Interior Designer Goal

● Your group’s goal is to design a theft-free convenience store by using mirrors instead of CCTV cameras.

Role

● Your group is a team of professional interior designers of commercial spaces.

Audience

● Your audience are your clients who are owners of a convenience stores located near the school community.

Situation

● Your group’s potential in designing commercial spaces attracted a convenience store owner who intends to minimize his expenditures in electronic surveillances such as using CCTV cameras.

Product, Purpose, Performance

● Your group will create a miniature model of a theft-free convenience store equipt with mirrors as replacement of CCTV cameras to minimize the client’s expenditures in electronic surveillances. The output will be a presentation of


the model of the interior design of the store. Standards and Criteria Your group’s performance will be based on the following rubrics.

Criteria Below Expectations, 0% to 49%

Needs Improvement

50% to 74%

Successful Performance 75% to 99%

Exemplary Performance

100%

Content. Detailed facts are presented well. Content related to the task.

Details not presented. Content is not related to the task.

Details are presented but not organized. There are some content that are not related to task.

Details are presented in an organized manner.Content are related to the task.

Details are presented in an organized matter that can be easily understood. Content are related to the task. Additional supporting details are presented.

Communication Skills. Presentation was done in a clear and logical manner.

Presentation was not done.

Presentation was done but in a disorganized and illogical manner.

Presentation was done smoothly but the concepts are presented in such a way that should be rearranged for better understanding.

Presentation was done clearly. Concepts were presented in a logical manner and easily understandable by the audience.

Self Check

Upon learning from this unit, can you now do the following:

Check I can…

discuss the reflection of light and law of reflection in mirrors

differentiate diffuse and specular reflection

differentiate plane, convex and concave mirrors

predict the type, orientation, and position of an image formed by plane, convex and concave mirrors through ray diagrams, mirror and


magnification equations

Key Words

Angle of incidence It is the angle which an incident ray makes with an imaginary line perpendicular to the surface.

Angle of reflection It is the angle which the reflected ray makes with the normal.

Center of curvature It is the point in the center of the sphere from which the curved mirror was sliced.

Concave mirror It is a curved mirror wherein the reflecting surface is on the inner surface of the sphere so that the center of the mirror sinks away from the viewer. It is also called a converging mirror.

Convex mirror It is a curved mirror wherein the reflecting surface is on the outer surface of the sphere so that the center of the mirror bulges towards the viewer. It is also called a diverging mirror.

Focal point It is the midpoint of the vertex and the center of curvature.

Orientation It is either an upright or inverted orientation of image produced by mirrors.

Plane mirror It is a smooth, reflecting surface.

Principal axis It is an imaginary line passing through the center of the sphere at the exact center of the mirror.

Real image It is the opposite of virtual images and can be projected on surface placed at the image position.

Reflection It is the bouncing of light when it reaches the boundary between two media.

Vertex It is the point where the principal axis and mirror meets.


Virtual image It is the image formed when light rays do not pass through the image location itself.

Key Formula

Concept Formula Description

Mirror equation

where:

● f is the focal length of the mirror

● p is the object distance ● q is the image distance

Mirror equation of different types of lenses

Use this formula to solve for focal length if the image and object distance are given.

Use this formula to solve for image distance if the focal length and object distance are given.

Use this formula to solve for object distance if the focal length and image distance are given.

Magnification

where: ● M is the magnification

power ● h’ is the image height

Use this formula to solve for magnification if image and object height given.


● h is the object height

where:

● M is the magnification power

● q is the image distance ● p is the object distance

Use this formula to solve for magnification if image and object distance given.

Wrap Up

Mirrors and Reflection of Light


Photo Credits

Unit Photo. Rear view mirror view in Mt. Rainier National Park, driving to Longmire (https://commons.wikimedia.org/wiki/File:Rear_view_mirror_view_in_Mt._Rainier_National_Park,_driving_to_Longmire.jpg) by Joe Mabel is licensed under CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0/legalcode) via Wikimedia Commons.

References

Serway, Raymond A. and Jerry S. Faugh. 2012. Physics. USA: Holt Giancoli, Douglas C. 2013. Physics: Principles with Applications 7th Edition. New Jersey:

Pearson Hugh D. Young, et al. 2012. Sears and Zemansky’s University Physics with Modern

Physics 13th Edition. California: Pearson Education Inc. The Physics Classroom. “Reflection and the Ray Model of Light.” Accessed May 1,

2017 at http://www.physicsclassroom.com/class/refln Mcdaniel College. “Convex and Concave Mirrors Activity.” Accessed May 2017 at

http://www2.mcdaniel.edu/Physics/LC%20Final%20version/Activity%2010%20-%20Results.doc.


http://www.physicsclassroom.com/class/refln

Answer Key

Lesson 8.2: Convex Mirrors

Let us Practice 1. The image will form at the back of the mirror. 2. The ray diagram is shown below.

3. The image is formed at the back of the mirror. It appears upright, diminished

(smaller) and it is a virtual image.

Lesson 8.3: Mirror Equation

Let us Practice 1. The mirror is a plane mirror. It has no focal point. 2. The image will form behind the mirror at a distance of 1.67 meters. 3. The image will form behind the mirror at a distance of 0.55 m. 4. The magnification is 1. It is a plane mirror. 5. The object was placed 60 cm away from the mirror. 6. Dave’s image is 0.52 m away from the mirror.

Lesson 8.4: Concave Mirrors

Let us Practice 1. The diagram is shown below.


2. The diagram is shown below.

3. Since the focal point is very small compared to the distance of the person,

you consider this to be a case where the object is at infinity distance as shown in the diagram below.


unit 8 reflection of light in mirrors

Documents