The Ray Model of Light Light from an object either results because the object is emitting light or light is reflecting from the surface of the object.

The Ray Model of Light

• Light from an object either results because the object is emitting light or light is reflecting from the surface of the object

The Ray Model of Light

• Light moves in straight lines, – simply draw a line to represent how the light

will behave– Perpendicular to the wave front of the light

wave

Reflection from a Plane Mirror

The angle of incidence equals the angle of reflection. This assumes the surface is perfectly smooth.

Diffuse Reflection

When the surface is rough, the surface at any point makes some angle w.r.t. the horizontal. The angle of incidence still equals the angle of reflection.

Plane Mirrors

In the left hand picture with a rough surface, you can place your eye anywhere and you will see some reflected rays. On the right hand side, you eye has to be in the correct position to see the reflected light. This is called specular reflection.

Plane Mirrors

A plane mirror provides the opportunity to fool you by making your eye and brain perceive an image.

Plane Mirrors

The image appears to be the same distance behind the mirror as the object is in front of the mirror.

Plane Mirrors

The image is called a virtual image because if you placed a piece of paper at the image location, you wouldn’t see any light.

How Big a Mirror?How long would a mirror have to be for you to see your shoes?

A. 1/4 your heightB. 1/2 your heightC. 3/4 your heightD. Your full heightE. It depends on where you stand.

Only half your height.

Spherical Mirrors

Again, we use the angle of incidence equals the angle of reflection. It is convenient to trace what happens to parallel light rays hitting the mirrors. Remember the definition of convex and concave!!

Spherical Mirrors

Precisely parallel rays do NOT meet at the same point after reflection from the surface of the mirror. Of course, precisely parallel rays only come from objects at huge distances away.

To avoid this problem and to form real images, we need to restrict ourselves to just a very small central region of the mirror.

Spherical Aberrationcauses fuzzy images.

Spherical Mirrors

In this limited region of the surface, the rays do intersect at the focus.

This picture defines the principal axis, the focal point and the focal length of the mirror. The line CB is a radius of the spherical surface. The focal point is at 1/2 the radius length.

Images in Spherical Mirrors

• Any ray parallel to the principal axis will pass through the focal point!

• Now we need to look at more rays leaving the same point on the object

Images in Spherical Mirrors

• Any ray from the object passing through the focal point will emerge parallel to the principal axis!!

Images in Spherical Mirrors

• Any ray striking the mirror at right angles will reflect straight back and will pass through the center of curvature!!

Images in Spherical Mirrors

• Now we want to derive an equation that will express the observations we have just made

Images in Spherical Mirrors

• The image and object distances are di and do

• The image and object heights are hi and ho

Images in Spherical Mirrors

• The right triangles I’AI and O’AO are similar (angles the same)

Images in Spherical Mirrors

€

hohi

=d0

di

Images in Spherical Mirrors

• Triangles O’FO and AFB are similar

• AB ≈ hi and FA = f (focal length)

Images in Spherical Mirrors

€

hohi

=OFFA

=do−ff

Images in Spherical Mirrors

€

hohi

=do−ff

=dodi

1do

+1di

=1f

Images in Spherical Mirrors

€

m=hiho

=−dido

Minus sign means upside down

Images in Spherical Mirrors

• Image is upright and virtual!

• Makeup Mirror

Images in Spherical Mirrors

• Passenger side outside car mirror

• Image is virtual and upright