Extended answer problem. Must to get credit! A camera lens in is illuminated by

Question

Extended answer problem. Must to get credit! A camera lens in is illuminated by light of wavelength 488nm. The index of refraction of the coating is 1.6. The refractive index of the lens is 1.75. The reflected light is observed. Reflection (a) What is the phase shift associated with the n1 and n2 (top) boundary (interface) for r_1. (b) What is the phase shift associated with the n2 and n3 (bouom) boundary (interface) for r_1? (c) What is the wavelength of the light in the coating film? (d) What is the path length difference between r_1 and r_2? Write your answer in terms of the length. L, given in the corresponding diagram above. (e) What phase shift needs to be provided by the path length difference in order to have destructive interference for the reflected light. (f) Calculate the thickness of the thinnest film necessary in order to have destructive interference for the reflected light. (g) Calculate the thickness of the thinnest film necessary in order to have constructive interference for the reflected light.

Explanation / Answer

a)     pi radians

b)   pi radians

c)    wavelength = 488/1.6 = 305 nm

d)    path length difference = 2L

e)       phase shift = 2pi/lambda * path difference

                             = pi/1.6   radians

f)     thickness of thinnest film for destructive interference =    (488)/(2 * 2 * 1.6)

                                                                                            =   76.25 nm

g)     thickness of thinnest film for constructive interference =    (488)/( 2 * 1.6)

                                                                                            =   152.5 nm

                                             

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