1 answer

Glass lens with antireflection coating

Question:

A glass lens (nglass = 1.52) has anantireflection coating of MgF2 (n = 1.38).

(a) For 639 nm light, what minimumthickness of MgF2 will cause the reflected raysR2 and R4 in the figuretointerfere destructively, assuming normal incidence?
(b) Interference will also occur between the forward-moving rays,R1 and R3 in the figure.What minimum thickness ofMgF2 will cause these two raysto interfere constructively?

Answers

We have
wavelength of light λ = 639*10-9mindex of refraction of MgF2 is n =1.38a)phase change for R2 =1/2phase change for R4 = 2nt / λ +1/2difference of phase changes is =2nt / λ +1/2- 1/2 = 2nt/λfor destructive interference we have2nt /λ = m + 1/2for minimum thickness m = 0so2nt / λ= 1/2or t =λ / 4nplug in for tb)phase change for R1 = nt/λphase change for R3 = 3nt / λ +1/2difference of phase changes = 3nt/λ +1/2 -nt/λ=2nt / λ +1/2forconstructive interference we have2nt /λ + 1/2 = mfor minimum thicknees m = 1so 2nt / λ = 1/2or t = λ /4nplug in for tHope this may help you ..

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