Mirrors

1. Mirrors Physics 202 Professor Lee Carkner Lecture 20

2. PAL #19 EM Waves • Laser from air to glass to water to glass to air q5 q4 q3 q1 q2 air n=1 glass n=1.52 water n=1.33 air n=1 glass n=1.52

3. PAL #19 EM Waves • To find each angle, n1 sin q1 = n2 sin q2 • sin-1 [(n1 / n2 )sin q1]= q2 • Input angle for each eqn is output angle from previous egn • q2 = sin-1 [(1 / 1.52)sin 20] = • q3 = sin-1 [(1.52 / 1.33)sin 13] = • q4 = sin-1 [(1.33 / 1.52)sin 15] = • q5 = sin-1 [(1.52 / 1)sin 13] =

4. 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

5. 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

6. 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

7. 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

8. 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

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

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

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

12. 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

13. 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

14. 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

15. 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

16. Next Time • Read: 34.7-34.8

17. What is the proper equation for I1? ½ I0 I0 cos290 I0 cos2 60 ½ I0 cos290 ½ I0 cos2 60

18. What is the proper equation for I2? ½ I1 I0 cos290 I0 cos2 60 ½ I0 cos290 ½ I0 cos2 60

19. What is the proper equation for I3? ½ I2 ½ I0 cos290 I0 cos2 60 cos2 60 ½ I0 cos260 cos2 30 ½ I0 cos2 60 cos2 60

20. If you removed the middle polarizer, what would be the intensity I3? 0 ½ I0 cos245 I0 cos2 60 cos2 60 ½ I0 cos260 cos2 30 ½ I0 cos2 60 cos2 60

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

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