Optics Question 870

Question: To produce a minimum reflection of wavelengths near the middle of visible spectrum (550 nm), how thick should a coating of $ MgF _{2}(\mu =1.38) $ coated on a glass surface?

Options:

A) $ {{10}^{-7}} $

B) $ {{10}^{-10}} $

C) $ {{10}^{-9}}m $

D) $ {{10}^{-8}}m $

Show Answer

Answer:

Correct Answer: A

Solution:

[a] The optical path difference needed for destructive interference is $ 2\mu d=(2n+1)\frac{\lambda }{2} $ , n-0, 1, 2, ?..

Note that 2nd is the total optical path length that the rays traverse when n=0.

$ \therefore d=\frac{\lambda /2}{2\mu }=\frac{\lambda }{4\mu }=\frac{350\times {{10}^{-9}}}{4\times 1.38} $

$ =100nm=1\times {{10}^{-7}}m $



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