Lecture 24-Lecture 24-11

Example: two polarizers

This set of two linear polarizers produces LP (linearly polarized) light. What is the final intensity?

– P1 transmits 1/2 of the unpolarized light:

I1 = 1/2 I0

– P2 projects out the E-field component parallel to x’ axis:

cos12 EE 2EI

2 22 1 0

1cos cos

2I I I = 0 if = /2

(i.e., crossed)

Lecture 24-Lecture 24-22 Image by Reflection from a Plane Mirror

• An extended object can be broken into infinite number of point objects.

• Image has the same height and orientation as the object.

Only small fraction of reflected rays received.

extended object

Virtual image at same distance from but on the other side of the mirror as the object•it is called a virtual image since no rays actually go through the image,

point object

r i

Lecture 24-Lecture 24-33 “Full Length” Mirror

1

2FG BC AC

1

2GH CD CE

1 1

2 2FH AC CE AE

Only half the object (and image) size is needed.

Lecture 24-Lecture 24-44Multiple Plane Mirrors

depth-inversion twice at P”12

“correct” image!

Lecture 24-Lecture 24-55

Non-scored test quiz – April 10, 2008

A person is standing still 2 meters in front of a mirror, then the mirror is moved 1 meter towards him and then stopped. What’s the distance between the person and his image before and after the mirror is moved?

a) 2m and 1m b) 3m and 2m c) 4m and 2md) 5m and 4m

Lecture 24-Lecture 24-66 Focal Point of a Spherical Mirror

When parallel rays incident upon a spherical mirror, the reflected rays or the extensions of the reflected rays all converge toward a common point, the focal point of the mirror. Distance f is the focal length.

Real focal point: the point to which the reflected rays themselves pass through. This is relevant for concave mirrors.

Virtual focal point: the point to which the extensions of the reflected rays pass through. This is relevant for convex mirrors.

f

f

Rays can be traversed in reverse. Thus, rays which (would) pass through F and strike the mirror will emerge parallel to the central axis.

concave mirror:

convex mirror

Lecture 24-Lecture 24-77Some Geometry

r

/ 2

cos 2

r r

2

rf

If is small, or rays are paraxial

2

, ,'

l l l

s s r

1 1 1

'

2

s rs f

mirror equation

Lecture 24-Lecture 24-88Locating Images

Real images form on the side of a mirror where the objects are, and virtual images form on the opposite side.

only using the parallel, focal, and/or radial rays.

Lecture 24-Lecture 24-99Mirror Equation and Magnification

' 'y sm

y s

'sm

s

• s is positive if the object is in front of the mirror (real object)

• s is negative if it is in back of the mirror (virtual object)

• s’ is positive if the image is in front of the mirror (real image)

• s’ is negative if it is in back of the mirror (virtual image)

• m is positive if image and object have the same orientation (upright)

• m is negative if they have opposite orientation (inverted)

• f and r are positive if center of curvature in front of mirror (concave)

• f and r are negative if it is in back of the mirror (convex)

1 1 1

's s f

(f = r/2)

Lecture 24-Lecture 24-1010Summary (for real object)

For concave mirrors ( f > 0):

• If the object is inside the focal point, the image is virtual (s’ < 0), enlarged, has the same orientation as the object and farther behind the mirror. The field of view is, therefore, smaller than that of a plane mirror

• If the object is outside the focal point, the image is real (s’> 0), inverted, reduced (or enlarged), and closer (or farther) to the mirror than the object.

• If the object is at the focal point, no image is formed.

For convex mirrors ( f < 0):• The image is always virtual (s’< 0), reduced, has the same orientation as the object and closer behind the mirror. The field of view is, therefore, larger than that of a plane mirror.

Lecture 24-Lecture 24-1111

Physics 241 –Quiz A

A man is standing still in front of a mirror, and the mirror is moved toward him at 1 m/s. What is the speed of the man’s image relative to the ground?

a) 0.5 m/sb) 1 m/sc) 1.5 m/sd) 2 m/se) 2.5 m/s

Lecture 24-Lecture 24-1212

Physics 241 –Quiz B

A mirror is standing still in front of a woman, andshe starts to walk toward the mirror at 1 m/s. Whatis the speed of the woman’s image relative to theground?

a) 0.5 m/sb) 1 m/sc) 2 m/sd) 2.5 m/se) 3 m/s

Lecture 24-Lecture 24-1313

Physics 241 –Quiz C

A man is standing still in front of a mirror, and the mirror is moved toward him at an unknown speed. If the speed of the man’s image relative to the ground is measured to be 2 m/s, what is the speed of the mirror relative to the ground?

a) 0.5 m/sb) 1 m/sc) 2 m/sd) 2.5 m/se) 3 m/s