Mirrors Physics 202 Professor Lee Carkner Lecture 22

PAL #21 EM Waves  Two polarizing sheets  I 1 = ½ I 0  I 2 = I 1 cos 2  1,2 = ½I 0 cos 2 90 = 0  No light gets through  One absorbs all x components, one absorbs all y components  Three polarizing sheets  I 1 = ½ I 0  I 2 = I 1 cos 2  1,2  I 3 = I 2 cos 2  2,3 = ½I 0 (cos 2  1,2 ) (cos 2  2,3 )  Since neither of the angles is 90, I 3 > 0  What is maximum intensity  When  1,2 =  2,3 = 45 degrees  I 3 = (0.5) I 0 (0.5)(0.5) = I 0

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 by 1/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:  Homework: Ch 34, P: 19, 27, 28, 29, 41, 45, 50, 51, 52, 54, 88