Mirrors Physics 202 Professor Lee Carkner Lecture 20

PAL #19 EM Waves  Laser from air to glass to water to glass to air air n=1 air n=1 glass n=1.52 glass n=1.52 water n=1.33 11 22 33 44 55

PAL #19 EM Waves  To find each angle, n 1 sin  1 = n 2 sin  2  sin -1 [(n 1 / n 2 ) sin  1 ]=  2   Input angle for each eqn is output angle from previous egn   2 = sin -1 [(1 / 1.52 ) sin  ] =   3 = sin -1 [(1.52 / 1.33 ) sin  ] =   4 = sin -1 [(1.33 / 1.52 ) sin  ] =   5 = sin -1 [(1.52 / 1 ) sin  ] =

Mirrors   Trace back the reflections of light from object O and it will converge to make image I   I is distance i from mirror   Images in the “real world” are called real

Plane Mirror   has curvature of infinity  Plane mirror images:   Are the same size as the object   Are the same distance behind the mirror as the object is in front of it i = -p  Note that distances “in the mirror” are negative

Spherical Mirrors   The center of curvature (C) is the center of the sphere that the mirror is a section of  A distance r from the mirror   The distance to the center of the mirror from the focal point is the focal length (f)  f = ½ r

Concave and Convex  Concave mirror:   The center of curvature is in front of the mirror   The image is larger than the object  Convex mirror:   The center of curvature is behind mirror   The image is smaller than the object

Ray Drawing  Can find image properties by drawing rays from object to image  First draw (to scale):   mirror (including curvature)   center of curvature (at r)   Follow ray drawing rules for two rays from top of object  Where they intersect is top of image

1) A ray that that is initially parallel to the central axis reflects through the focal point

2) A ray that passes through the center of curvature reflects back along itself

3) A ray that reflects from the mirror at the intersection with the central axis reflects symmetrically about the central axis

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 back side of the mirror i and f are negative  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  For m = 1, image and object are same size   For |m| < 1, image is smaller  If m is negative, image is inverted

Concave   Produces a upright, virtual image  Concave mirrors are used to provide magnification (e.g. a shaving or make-up mirror)   Produces an inverted, real image  A real image is projected onto something, it is not behind the mirror

Convex  For a convex mirror:  The center of curvature is behind the mirror   The image is closer to the mirror (|i| < p)  The image is smaller than the object 

Next Time  Read:

What is the proper equation for I 1 ? A)½ I 0 B)I 0 cos 2  C)I 0 cos 2 6  D)½ I 0 cos 2  E)½ I 0 cos 2 6 

What is the proper equation for I 2 ? A)½ I 1 B)I 0 cos 2  C)I 0 cos 2 6  D)½ I 0 cos 2  E)½ I 0 cos 2 6 

What is the proper equation for I 3 ? A)½ I 2 B)½ I 0 cos 2  C)I 0 cos 2 6  cos 2 6  D)½ I 0 cos 2  cos 2 3  E)½ I 0 cos 2 6  cos 2 6 

If you removed the middle polarizer, what would be the intensity I 3 ? A)0 B)½ I 0 cos 2  C)I 0 cos 2 6  cos 2 6  D)½ I 0 cos 2  cos 2 3  E)½ I 0 cos 2 6  cos 2 6 

What is the direction of polarization of polarized sunglasses? A)Left - right B)Up - down C)At a 45 degree angle to the vertical D)One lens is up-down and one is left right E)They could be polarized in any direction

Do polarized sunglasses work on light that is not glare (not reflected)? A)No, the goggles do nothing B)Yes, but only if the light is polarized in some other way C)Yes, but they only reduce the light by a small amount D)Yes, they make unpolarized light half as bright E)No, but they still look cool