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I’m Dr Alex Pettitt, and I’ll be your guide!

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Physics I:

Lecture 13: 13-11-2020

Mirrors and lenses

Light ray hits surface

Light ray hits surface

Ray moves away from surface

Ray enters object and changes speed & direction.

Reflection & RefractionLast lecture:

✓01 = ✓1

Reflection:

✓1

✓01

Refraction:

✓1✓2

n1 sin ✓1 = n2 sin ✓2

Now is a good time to go try:

Class 13: review

Optics

Mirrors and lenses

Plane mirror

Plane (flat) Mirrors

Eye assumes light rays are straight

Light from the triangle reflects off the mirror to the eye.

‘Sees’ the triangle behind the mirror.

Image is virtual : no light actually comes from behind the mirror.

Object Image

behi

nd m

irror

Plane MirrorsWhere is the image?

??Height?

??

Distance from mirror?

I’ll just use an arrow to represent an arbitrary object. be

hind

m

irror

Object Image

Plane mirror

Plane Mirrors2 light rays needed to locate each point in the mirror.

arrow to mirror distance = image to mirror distance

Rays top and bottom of arrow are normal to mirror and parallelimage is same height as arrow

locate arrow bottom

locate arrow top

behi

nd

mirr

or

Object Image

congruent triangles(sides & angles equal)

O O’P

Q

Plane mirror

Plane Mirrors

Plane mirror image has same length and orientation (not upside down) as object.

But reverse the object front-to-back*.

Your right hand looks like your left hand.

*better to think of it as a “front to back:, not

“right to left"

Curved MirrorsParabolic curved mirror:

✓

✓

axis focal point

If ray is parallel to axis,

it will be reflected through the focal point/focus.

angle with normal angle with line to focal point

=

Can concentrate light at the focal point

or put light source at the focal point and get parallel rays

Curved MirrorsParabolic curved mirror:

axis focal point

If ray is parallel to axis,

angle with normal angle with line to focal point

=

it will be reflected through the focal point/focus.

Can concentrate light at the focal point

or put light source at the focal point and get parallel rays

Curved Mirrors

✓

✓

axis focal point

Close to apex, mirror looks spherical.

Easier to make spherical mirrors

slight image distortion: spherical aberration

most focussing mirrors are spherical.

Famous example: Hubble Space Telescope

Mirror made with wrong curve, big spherical aberration.

Curved Mirrors

focal length

Focal length >> mirror

Rays strike the mirror ~ parallel to axis paraxial approximation

To minimise spherical aberration:

Mirror small fraction of whole sphere

Curved MirrorsTo find image draw 2 rays from different points on the object.

Any ray possible, but these are simplest:

(1) A ray parallel to the mirror axis reflects through the focal point.

(2) A ray passing through the focal point reflects parallel to the axis.

(3) A ray striking the center of the mirror reflects symmetrically about the mirror axis.

(4) A ray through the centre of curvature of the mirror returns on itself.

FC

1

2

3

4

Curved MirrorsExamples:

Locate image top with 2 rays (types 1 & 2)

From symmetry, bottom of image is on the axis.

Light rays come from the image and converge as a real image

(check rays 3, 4 also make sense!)

FC

O

I

Real, inverted, reduced

Object outside of C results in smaller image.

Curved MirrorsExamples:


move object closer to mirror

As object gets closer to mirror, image size increases.

When object is between mirror centre (C) and focus point (F), image is larger than object and further away.


FC

I

O

Light rays come from the image: real image

Curved Mirrors

What does a real image look like?


Curved MirrorsExamples: move object closer to mirror

Image is upright and enlarged.

Rays diverge (go apart) after reflection.

Appear to cross behind the mirror


FCIO

Light rays do not come from the image: virtual image

Curved Mirrors

Curved MirrorsConvex mirrors

Reflected rays diverge

Only forms virtual images

FO

Reflected parallel rays appear to come from the focal point behind the mirror, F

Image is always upright (not inverted) and smaller.

Used to image large area in small space (wide angle view)

I

Curved MirrorsConvex mirrors

Curved MirrorsReal vs virtual:

Real image: rays converge.Actual photons travel the path, and are collected at I.You can project image onto a screen.

Virtual image: rays diverge.No photons travel the path, light is dispersed.You cannot project image onto a screen.

FO I

FC

O

I

Now go and try: Class 13: quiz 1

C F

Mirror EquationDrawing rays works....

... but can we be more accurate?

2 rays (type 1 & 3)

Similar triangles:

�h0s0

h

s

M =h0

h= �s0

s(magnification)

inverted image: negative h’

(virtual image: negative s’)Here, because image is smaller|M | < 1

and negative, because image is inverted

s and s’ both >0.

h

sO

s’

-h’

Mirror EquationDrawing rays works....

... but can we be more accurate?

2 rays (type 1 & 3)

Similar triangles #2 :

h

f�h0s0 � f

�h0

h=

(s0 � f)

f

s0

s=

(s0 � f)

f

1

s+

1

s0=

1

fmirror equation

M = h0/h = �s0/s

C F-h’

h

O

I f

s’ - f

s’

h

Mirror Equation

If image is virtual: s0 < 0

image distance is negative

f < 0If mirror is convex:

1

s+

1

s0=

1

f

Mirror Equation Example

The Hubble Space Telescope has a mirror with 5.52 m focal length.

A man stands 3.85 m in front of the mirror.

What is the (a) location (b) magnification of the image?

1

s+

1

s0=

1

fmirror equation:

s0 =fs

s� f=

(5.52m)(3.85m)

3.85m� 5.52m

= �12.7m


The Hubble Space Telescope has a mirror with 5.52 m focal length.

A man stands 3.85 m in front of the mirror.

What is the (a) location (b) magnification of the image?

M = �s0

s= ��12.7m

3.85m= 3.30

Mirror Equation1

s+

1

s0=

1

f2f = RRemember the point of C is at:


Jurassic Park

OBJECTS IN MIRROR ARE CLOSER THAN THEY SEEM.


If the mirror’s curvature radius is 12 m and the T. rex is 9.0 m away, what is its magnification?

1

s+

1

s0=

1

fmirror equation: s0 =

fs

s� f

M = �s0

s= �fs/(s� f)

s= � f

s� f

= � (�6.0m)

9.0m� (�6.0m)= 0.4

|f | = R/2 = �6.0mand

40% of actual size, so seems to be further away.

≈ç≈ç

Lenses

LensesA lens uses refraction to form images.

Because lenses refract, not reflect, this is opposite to mirrors.

Convex lens that focusses parallel rays to the focal point

Converging lens

Concave lens: parallel rays seem to move away from a common focus.

Only forms virtual images.

Diverging lens

LensesThin lens approximation

Thickness << curvature radius

Although the ray refracts twice (as it enters lens and as it exits) single refraction

thin lens

Rays can pass through a lens in 2 directions

Focal length is the same both sides.

LensesRay through lenses

(1) Ray parallel to lens axis refracts through the focal point.

(2) Ray passing through the centre travels straight, no deflection.

Use these two rays to find images formed with lenses.

F F

1

2

LensesExample #1

Object further than two focal lengths, s > 2f

Image smaller and inverted.

Light rays come from the image: real image

(do not need to look through lens to see images)

f2fs >2f

Of 2f

I

LensesExample #2

Decrease the distance of object to lens.

Image becomes larger and further away, still inverted.

2f

f 2f

O

2f < s < f

f

f 2f I

LensesExample #3

Image large and virtual:

Object closer than focal length, s < f

rays do not come from image

Can only be seen looking through the lens.

f fs < f

O

I

Lenses

Lenses

Concave (diverging) lens always forms a smaller, upright image.

Only visible through the lens.

The lens equation

s

h

Similar triangles: M =h0

h= �s0

s

(same as mirrors)

Magnification

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F

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The lens equation

f

s0 � f

Similar triangles #2: �h0

s0 � f=

h

f

1

s+

1

s0=

1

flens equation (same as mirror equation)


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The lens equation

The lens equation Example

You use a magnifying glass with a 30-cm focal length to read.

How far from the page should you hold the lens to see the print enlarge x 3?

=1

f=

1

30cm

s =(2)(30cm)

3= 20cm

M = �s0

s= 3 s0 = �3s

1

s+

1

s0=

1

f

1

s� 1

3s=

2

3s

Example 1: eyesEye focuses light on the retina on the back of the eyeball.

Lens can change shape to alter f.

FarsightedNearsighted

An extra lens can be used to correct problems with eyes:

Example 2: micro/telescopesUsed to enlarge images.

First lens magnifies and flips the image.

The second places a virtual image at a large distance so the eye can focus.

Telescopes similar, but the object is much further away!

There are also “reflecting” telescopes. object at infinity focuses on f

Focus by changing L

Lecture 13 : Summary

Geometrical optics: drawing propagation lines for the path light travels.

Differences between real and virtual images.

Mirrors and lenses, their similarities and differences.

The mirror and lens equations:s s’

h h’f

1

s+

1

s0=

1

flens equation

1

s+

1

s0=

1

fmirror equation

M =h0

h= �s0

s(magnification)

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