1. Suppose you are hired to work in an optics lab which utilizes green laser light at 19\

l. Suppose you are hired to work in an optics lab which utilizes green laser light at A = 532nm green for performing a particular optical experiment. If you could reduce reflections from the lens, you could also reduce error in your experiment. You decide to apply an optical coating to your lens, but you need to determine how thick the coating should be to minimize reflections. The index of 2.0, the index of refraction for the lens is = 1.5 and refraction of the optical coating is = = 1.0. Let the thickness of the coating be represented by the the index of refraction for air is letter d. A. (5 points) Draw a diagram (like the one done in class) which illustrates light traveling through air, the coating and your lens. Show the reflection and transmission of the light at each boundary. Be Sure to label the index of refraction of each medium and any other relevant information for the problem. Make a list of knowns and unknowns. B. (5 points) Explain in words what happens to the laser light as it passes the discontinuity between air and the optical coating. Explain in words what happens to the laser light as it passes the discontinuity between the optical coating and the lens. Are the two reflected waves "in phase" or "out of phase" with each other? Explain. Be sure to label any phase shifts on your diagram in part (a). C. (5 points) The coating you are using is very expensive, so you want it to be as thin as possible. Derive a symbolic expression for the depth d of the thinnest possible coating that will eliminate reflections of the incoming green laser light. D. (5 points) Check the validity of your expression from part C using at least two sensemaking techniques learned in class then evaluate this expression to find the depth d in nanometers. Evaluate this expression to find the depth d in nanometers. E. (5 points) Suppose you use the lens coated for green light for an experiment which uses red laser light at Ired = 633nm. Do the reflected waves interfere constructively, destructively or somewhere in between? Explain in a sentence or two. (Hint: To back up your answer, it may be helpful to find the phase difference of the two reflected waves in terms of IT).