Magnification, Refraction and Snell’s Law

Warning – Lots of Math Required for this Lesson!

SNC2D

Review Significant DigitsNon-zero digits are always significant!Zeroes placed before other digits are not

significant; 0.046 has two significant digitsZeroes placed between other digits are

always significant; 4009 kg has four significant digits

Zeroes placed after other digits but before a decimal point are NOT significant; 7600 has two significant digits.

Zeroes placed after other digits but after a decimal point are significant; 7.90 has three significant digits

Review of Scientific Notation!4.5 x 10-4 means…

5.6 x 105 means…

the decimal place is moved to the LEFT 4 places

= 4.5 x 10-4 means 0.00045

the decimal place is moved to the RIGHT 5 places

= 5.6 x 105 means 560 000

Converting to Scientific Notation

When writing in scientific notation we need to be aware of the significant digits. This will determine the first number in our term.

Example 1: 546 000 is written as 5.46 x 105

Example 2: 0.0073 is written as 7.3 x 10-3

Example 3: 5008 is written as 5.008 x 103

MagnificationMagnification is the measure of how much

larger or smaller an image is compared with the object itself.

It is expressed as a ratio of height of the image (hi) to the height of the object (ho) .

• M = hi / ho

It can also be determined by taking the ratio of the distance from the image (di) to the mirror and the distance from the object (do) to the mirror

• M = di / do

Magnification Cont’dRemember to use the same units of

measurement in each ratio!

Your final answer will not include any units because they end up cancelling each other out.

If the Magnification factor is greater than 1, the image will be bigger than the object.

If the Magnification factor is less than 1, the image will be smaller than the object.

Magnification Examples

Example 2: A concave mirror creates a virtual image of a candle flame that is 6 cm high. If the magnification of the mirror is 2.5, what is the height of the candle flame?

We are given height and magnification… M = hi / ho rearrange to get the formula… ho = hi / M = 6 cm / 2.5 = 2.4 cm

Example 1: An object is placed 60 cm from a concave mirror. An image is produced 45 cm away. What is the magnification?

We are given distance… M = di / do = 45 cm / 60 cm = 0.75 or 7.5 x 10-1

RefractionRefraction - The bending of light rays as they

pass through two different media (plural for medium)

Light travels very fast - 3.0 x 108 m/s in a vacuum

Light travels slower when it is moving through a medium (air, water, carbon dioxide, table salt, etc.)

Refraction occurs when light Enters a medium and also when it Leaves a medium.

Index of RefractionThe amount by which a transparent medium

decreases the speed of light is called refraction.

The larger the refractive index, the more the medium decreases the speed of light

Speed of light in a vacuum is 3.0 x 108 m/s. This is the fastest that light can travel, therefore it is given a Refractive Index of 1.00.

Table 11.5 Index of Refraction

Page 437 in your textbook!

Index of Refraction FormulaSpeed of light in a vacuum is denoted with a small

letter c

Speed of light in a medium is denoted with a small letter v

The Refractive Index is denoted with a small letter n

The formula we use for index of refraction is n = c / v

In words: The index of refraction is equal to the speed of light in a vacuum divided by the speed of light in the medium

Index of Refraction ProblemsExample 1: The speed of light in leaded

glass is 1.66 × 108 m/s. What is the index of refraction of this type of glass?

n = c / v where c = speed of light in a vacuum = 3.0 x 108 / 1.66 x 108 = 3.0 x 108 m/s = 1.8 v = 1.66 x 108 m/s (given)

n = looking for

Therefore, the index of refraction for leaded glass is 1.8.

Index of Refraction ProblemsExample 2: What is the speed of light

through sapphire?

n = c / v where c = speed of light in a vacuum 1.77 = 3.0 x 108 / v = 3.0 x 108 m/s 3.00 x 108 / 1.77 = v v = looking for 1.69 x 108 m/s = v n = 1.77 (table from pg. 435)

Therefore, the speed of light through sapphire is 1.69 x 108 m/s

DispersionAs white light enters a water droplet, each

wavelength of light gets refracted at slightly different angles.

The light gets refracted twice:Once when it enters the water dropletOnce when it leaves

Introduction to Snell’s Law

If the light strikes the surface of the water at an angle, that part of the light beam that enters first will slow down first.

1.003

1.61

Introduction to Snell’s Law

When light travels from air, with a low refractive index, into water, with a higher refractive index, it bends toward the normal

When light travels from a higher refractive index medium into a lower refractive index medium, it bends away from the normal

The angle of incidence, θi, and the angle of refraction, θR, are measured from the normal.

Introduction to Snell’s Law

Snell’s LawSnell’s law is a formula that uses values for

the index of refraction to calculate the new angle that a ray will take as a beam of light strikes the interface between two media:

n1sinθ1 = n2sinθ2

The indices of refraction of two different media are indicated as n1 and n2 and the angles of incidence and the angle of refraction are indicated as θ1 and θ2

Snell’s Law ExamplesExample 1: When light passes from air into water

at an angle of 60° from the normal, what is the angle of refraction?Solution:

Snell’s Law ExamplesExample 2: In an experiment, a block of cubic zirconia is placed

in water. A laser beam is passed from the water through the cubic zirconia. The angle of incidence is 50°, and the angle of refraction is 27°. What is the index of refraction of cubic zirconia?

Solution:

Seatwork QuestionsPage 424 – 2 questions from EACH sectionPage 425 – 2 questions from EACH sectionPage 438 – All Practice Questions (except for

the two we have already covered)Page 441 – Practice Questions #1,2,3Page 442 – Practice Questions #1,2,3