(9%) Problem 12: A ray of light is incident on an air/water interface. The ray makes an angle of 191 = 45 degrees with respect to the normal of the surface. The index of the air is n1 = 1 while water is n2 = 1.33. 25% Part (3) Choose an expression for the angle (relative to the normal to the surface) for the ray in the water, 62. 62 = asin (sin(51) :li) V Correct! A 25% Part (b) Numerically, what is the angle in degrees? 02:1 sin() cos() tan() :1: ( 7 3 | 9 cotan() asin() acos() E 4 5 | 6 atan() acotan() sinh() 1 3 cosh() tanh() cotanh() + 0 | . ODegrees Radians do I Submit | Hint | | Igive up! | Hints: deduction per hint. Hints remaining: _ Feedback: deduction per feedback. Grade Summary Deductions Potential 100% Submissions Attempts remaining: _ (_ per attempt) detailed View A 25% Part (c) Write an expression for the reection angle 1/}, with respect to the surface. A 25% Part ((1) Numerically, what is this angle in degrees? (7%) Problem 13: Consider the situation in the gure - a student diver in a pool and an instructor on the edge, outside the water. Since the indices of refraction of air and water are different, the light rays coming from the diver and the instructor are refracted at the surface, changing their apparent position with respect to each other. The diver sees the instructor at an apparent angle of 0a = 22, measured from the normal to the interface. , - l i i a, Randomized Variables 0,:22" 7,; V 5,, , Kilhccxpcrt[axon] A 50% Part (2) Find the height of the instructor's head above the water in meters, noting that you will rst have to calculate the angle of incidence (you can take the indices of refraction to be nQ = 1 for air and nE = 1.33 for water). select pan Grade Summary h = I Deductions Potential 100% sin() cos() tan() 7: ( 7 9 | illltbmislsions ' _ . emp S remaining: cotan() as1n() acos() E 4 5 6 I (_ per attempt) atan() acotanO sinho 1 2 3 I detailed view cosh() tanh() cotanhO + - 0 . | 0 Degrees Radians do Submit | Him | | I give up! | Hints: deduction per hint. Hints remaining: _ Feedback: deduction per feedback. Q 50% Part (b) Find the apparent depth of the diver's head below water as seen by the instructor in meters, assuming the diver and his image both have the same horizontal distance along the surface of the water. (5%) Problem 14: Fiber optics are an important part of our modern internet. In these fibers, two different glasses are used to confine the light by total internal reflection at the critical angle for the I cladding interface between the core (ncore = 1.489 ) and the cladding (ncladding = 1.447). n core 50% Part (a) Numerically, what is the largest angle (in degrees) a ray will make with respect to the interface of the fiber Omar, and still experience total internal reflection? Grade Summary max = Deductions 0% Potential 100% sin() cos tan( 7 8 9 HOME Submissions Attempts remaining: 100 cotan() asin() acos() E A 5 6 (0% per attempt 2 detailed view atan() acotan() sinh() 3 each () tanh() cotanh( ) + END atan () Degrees O Radians VO BACKSPACE DEL CLEAR Submit Hint Feedback I give up! Hints: 2% deduction per hint. Hints remaining: 2 Feedback: 2% deduction per feedback. 4 50% Part (b) Suppose you wanted the largest angle at which total internal reflection occurred to be max = 5 degrees. What index of refraction does the cladding need to be if the core is unchanged