Mirrors

Physics 202Professor Lee

CarknerLecture 22

PAL #21 EM Waves Two polarizing sheets

I1 = ½ I0 I2 = I1 cos2 1,2 = ½I0 cos2 90 = 0 No light gets through One absorbs all x components, one absorbs

all y components Three polarizing sheets

I1 = ½ I0 I2 = I1 cos2 1,2

I3 = I2 cos2 2,3 = ½I0 (cos2 1,2) (cos2 2,3) Since neither of the angles is 90, I3 > 0

What is maximum intensity When 1,2 = 2,3 = 45 degrees I3 = (0.5) I0 (0.5)(0.5) = 0.125 I0

What is an Image?

When you see an object, your eye gathers light rays that are reflected off of it and your brain processes it into an image

If the light is refracted or reflected, you see an image of the object at a position different from the actual

Types of Images

Virtual image

This is a virtual image

Real image If you project an image onto a surface it is

called a real image

Plane Mirrors

The images appear to be at a

point behind the mirror

Light rays will hit the mirror and then reflect at some angle

If you trace the reflections back through the mirror they intersect at point I, the image location

Location of Image The object is at a distance p

from the front of the mirror and the image is a distance i behind the mirror and the angle between the reflected ray and the normal is

i = -p The image is the same distance

behind the mirror as the object is in front of it

Extended Objects

Each point in the image is directly in front of its actual position

Example: when you move your right hand your image appears as a person moving his left hand

Spherical Mirrors

A spherical mirror can either be concave (curved in towards the object) or convex (curved out away from the object)

A distance r from the mirror The field of view is the area that the mirror

reflects

Concave

For a concave mirror:

The field of view is smaller than that of a plane mirror

The image is farther behind the mirror (|i| > p)

Concave mirrors are used to provide magnification (e.g. a shaving or make-up mirror)

Convex

For a convex mirror:

The field of view is larger than that of a plane mirror

The image is smaller than the object

Convex mirrors are used to view large areas (e.g. car side mirrors, security mirrors)

Focal Point If an object is located an infinite distance

from the mirror (e.g. a star) than the light rays are all parallel when they are incident on the mirror

For a concave mirror all of the light is focused to a point after reflection, called the focal point or focus The distance to the center of the mirror from

the focal point is the focal length (f)

Focal Point and Convex Mirrors

If you trace back the rays they meet at a point behind the mirror called the virtual focus

For either mirror the radius of curvature r (the radius of the sphere or the distance to the center of curvature C) is related to the focal length by:

f = ½ r

Images and Concave Mirrors

When the object is in front of the focal point (closer to the mirror) a virtual image appears in the mirror

When the object is behind the focal point (further from the mirror) the mirror will project a real image in front of the mirror A real image is projected onto

something, it is not behind the mirror

Mirror Equation Where are the images and how large are they?

When measuring from the center of the mirror:

i is the distance to the image

when I and F are on the other side of the mirror i and f are negative

They are related by1/p + 1/i = 1/f

Magnification If h is the height of the object and h’ is the

height of the image then the magnification is given by:

|m| = h’/h

m = -i/p when m is negative, the image is inverted with

respect to the object Remember that i can be positive or negative

Ray Drawing If you draw two different rays from an

object the image will appear at the intersection of the rays

An extended object can be found by drawing several pairs of rays

When trying to find an image it often helps to draw rays based on 3 rules:

1)

2)

3)

Next Time

Read: 34.7-34.8 Homework: Ch 34, P: 19, 27, 28,

29, 41, 45, 50, 51, 52, 54, 88