IVB. Geometric optics 2. Reflection 1. Wave front and rays 3. Refraction: Snell’s Law index of refraction: rays wave fronts Example: n1n1 n2n2 n3n3 inout normal to surface diffuse reflection 1

Example: 2

4. Total internal reflection Example: 3

1) Binoculars often use total internal reflection; this gives true 100% reflection, which even the best mirror cannot do. 4a. Applications of total internal reflection 2) Fiber optics. The typical value of the index of refraction for optical fibers: for the core n=1.48 for the cladding n= An image can be formed using multiple small fibers Light will be transmitted along the fiber even if it is not straight

5. Plane mirror O I dodo didi O I dodo didi Image in plane mirror: virtual erect the same size d o = d i 6. Comments about objects and images created by different optical instruments: curved mirrors, lenses and their combinations Image: real or virtual erect or inverted lager, smaller, or the same size as the object h o = h i 5

7. Spherical mirror 1) Mirror equation Cdidi dodo h Example: 6

2) Magnification C didi dodo Example: What is magnification in the previous example? This image is real, inverted, and 5 times smaller than the object 7

3) Graphical method 8

4) Image and object at various distances CF C F 0f=R/2 2f=R 9

magnificationimagemirror d o didi m<0inverted, realconcaved o >fd i >f m>1 0<m<1 upright, virtualconcave convex 0<d o <f 0<d o d i <0 -f<d i <0 10

Example: You are standing 3.0 m from a convex security mirror in a store. You estimate the height of your image to be half of your actual height. Estimate the radius of curvature of the mirror. 11

Example: The magnification of a convex mirror is for objects 2.2 m from the mirror. What is the focal length of this mirror? 12

Example: A shaving/makeup mirror is designed to magnify your face by a factor of 1.33 when your face is placed 20.0 cm in front of it. (a)What type of mirror is it? (b) Describe the type of image that it makes of your face. (c) Calculate the required radius of curvature for the mirror. Solution: (a) To produce a larger image requires a concave mirror. (b) The image will be erect and virtual. (c) 13

Example1: Concave spherical mirrors produce images which A) are always smaller than the actual object B) are always larger than the actual object C) are always the same size as the actual object D) could be smaller than, larger than, or the same size as the actual object, depending on the placement of the object Example2: Convex spherical mirrors produce images which A) are always smaller than the actual object B) are always larger than the actual object C) are always the same size as the actual object D) could be larger than, smaller than, or the same size as the actual object, depending on the placement of the object Example3: A single concave spherical mirror produces an image which is A) always virtual B) always real C) real only if the object distance is less than f D) real only if the object distance is greater than f Example4: A single convex spherical mirror produces an image which is A) always virtual B) always real C) real only if the object distance is less than f D) real only if the object distance is greater than f 14