Light very often travels in straight lines. We represent light using rays, which are straight lines emanating from an object. This is an idealization,

Light very often travels in straight lines. We represent light using rays, which are straight lines emanating from an object. This is an idealization, but is very useful for geometric optics.

The Ray Model of LightThe Ray Model of Light

Law of reflection: the angle of reflection (that the ray makes with the normal to a surface) equals the angle of incidence.

Reflection; Image Formation by a Plane MirrorReflection; Image Formation by a Plane Mirror

Law of ReflectionLaw of Reflection

1A

B

Mirror

FermatFermat’’s Principles Principle

Using Fermat’s Principle you can prove theReflection law. It states that the path taken by light when traveling from one point to another is the path that takes the shortesttime compared to nearby paths.

JAVA APPLET

Show Fermat’s principle simulatorhttp://www.phys.hawaii.edu/~teb/java/ntnujava/index.html

Two light rays 1 and 2 taking different Two light rays 1 and 2 taking different paths between points A and B and paths between points A and B and

reflecting off a vertical mirrorreflecting off a vertical mirror

1

2

A

B Plane Mirror

Use calculus - method of minimization

Write down time as a function of yand set the derivative to 0.

When light reflects from a rough surface, the law of reflection still holds, but the angle of incidence varies. This is called diffuse reflection.

Reflection; Image Formation by a Plane MirrorReflection; Image Formation by a Plane Mirror

With diffuse reflection, your eye sees reflected light at all angles. With specular reflection (from a mirror), your eye must be in the correct position.

Reflection; Image Formation by a Plane MirrorReflection; Image Formation by a Plane Mirror

Reflection; Image Formation by a Plane MirrorReflection; Image Formation by a Plane Mirror

Example 32-1: Reflection from flat mirrors.

Two flat mirrors are perpendicular to each other. An incoming beam of light makes an angle of 15° with the first mirror as shown. What angle will the outgoing beam make with the second mirror?

What you see when you look into a plane (flat) mirror is an image, which appears to be behind the mirror. This is called a virtual image, as the light does not go through it. The distance of the image from the mirror is equal to the distance of the object from the mirror.

Reflection; Image Formation by a Plane MirrorReflection; Image Formation by a Plane Mirror

Reflection; Image Formation by a Plane MirrorReflection; Image Formation by a Plane Mirror

Example : How tall must a full-length mirror be?

A woman 1.60 m tall stands in front of a vertical plane mirror. What is the minimum height of the mirror, and how close must its lower edge be to the floor, if she is to be able to see her whole body? Assume her eyes are 10 cm below the top of her head.

ConcepTest 32.1ConcepTest 32.1 ReflectionReflection

When watching the Moon over

the ocean, you often see a long

streak of light on the surface of

the water. This occurs because:

1) the Moon is very large

2) atmospheric conditions are just right

3) the ocean is calm

4) the ocean is wavy

5) motion of the Moon

When the water surface changes, the angle of angle of

incidence also changesincidence also changes. Thus, different spots different spots

on the water can reflect the Moonon the water can reflect the Moon into your into your

eyes at different timeseyes at different times.

ConcepTest 32.1ConcepTest 32.1 ReflectionReflection

When watching the Moon over

the ocean, you often see a long

streak of light on the surface of

the water. This occurs because:

1) the Moon is very large

2) atmospheric conditions are just right

3) the ocean is calm

4) the ocean is wavy

5) motion of the Moon

Follow-up:Follow-up: Where else does this occur? Where else does this occur?

ConcepTest 32.2aConcepTest 32.2a Mirror IMirror I

S

O

1

2

3

4

mirrorAn observer at An observer at point Opoint O is facing a is facing a

mirror and observes a mirror and observes a light source light source

SS. Where does the observer . Where does the observer

perceive the mirror image of the perceive the mirror image of the

source to be located?source to be located?

ConcepTest 32.2aConcepTest 32.2a Mirror IMirror I

S

O

1

2

3

4

mirror

Trace the light rays from the object

to the mirror to the eye. Since the

brain assumes that light travels in a

straight line, simply extend the rays

back behind the mirror to locate the

image.

An observer at An observer at point Opoint O is facing a is facing a

mirror and observes a mirror and observes a light source light source

SS. Where does the observer . Where does the observer

perceive the mirror image of the perceive the mirror image of the

source to be located?source to be located?

Follow-up:Follow-up: What happens when the observer starts moving What happens when the observer starts moving toward the mirror?toward the mirror?

ConcepTest 32.2bConcepTest 32.2b Mirror IIMirror II

You stand in front of a You stand in front of a

mirror. How tall does the mirror. How tall does the

mirror have to be so that mirror have to be so that

you can see yourself you can see yourself

entirely?entirely?

1) same as your height

2) less than your full height but more than half your height

3) half your height

4) less than half your height

5) any size will do

ConcepTest 32.2bConcepTest 32.2b Mirror IIMirror II

Trace the light rays from the image

’s foot to the mirror and then to

the eye. Since we know that ii = =

rr , you need a mirror only half mirror only half

your sizeyour size.

You stand in front of a You stand in front of a

mirror. How tall does the mirror. How tall does the

mirror have to be so that mirror have to be so that

you can see yourself you can see yourself

entirely?entirely?

1) same as your height

2) less than your full height but more than half your height

3) half your height

4) less than half your height

5) any size will do

ConcepTest 32.2cConcepTest 32.2c Mirror IIIMirror III

Does this depend on your Does this depend on your

distance from the mirror?distance from the mirror?

1) no

2) yes

3) depends on the mirror

4) depends on the person

ConcepTest 32.2cConcepTest 32.2c Mirror IIIMirror III

Does this depend on your Does this depend on your

distance from the mirror?distance from the mirror?

The farther you step back, the

smaller the incident and

reflected angles will be. But the

rays will still be reflected at the

same points, so the ray from

the foot will still be reflected at

mid-height.

1) no

2) yes

3) depends on the mirror

4) depends on the person

ConcepTest 32.3ConcepTest 32.3 All Smoke and MirrorsAll Smoke and Mirrors

1.0 m 0.5 m

1) 0.5 m

2) 1.0 m

3) 1.5 m

4) 2.0 m

5) 2.5 m

You hold a hand mirror You hold a hand mirror 0.5 m0.5 m in in

front of you and look at your front of you and look at your

reflection in a full-length mirror reflection in a full-length mirror 1 m1 m

behind you. behind you. How far in back of the How far in back of the

big mirror do you see the image of big mirror do you see the image of

your face?your face?

The image of the face reflected in the

small mirrorsmall mirror appears 0.5 m0.5 m behind the

small mirror. This image (which is

the object for the big mirrorbig mirror) is 2.0 m2.0 m

away from the big mirror. The final

image is 2.0 m2.0 m behind the big mirrorbig mirror.

ConcepTest 32.3ConcepTest 32.3 All Smoke and MirrorsAll Smoke and Mirrors

1.0 m 0.5 m

1) 0.5 m

2) 1.0 m

3) 1.5 m

4) 2.0 m

5) 2.5 m

You hold a hand mirror You hold a hand mirror 0.5 m0.5 m in in

front of you and look at your front of you and look at your

reflection in a full-length mirror reflection in a full-length mirror 1 m1 m

behind you. behind you. How far in back of the How far in back of the

big mirror do you see the image of big mirror do you see the image of

your face?your face?