Question

A silicon monoxide (n = 1.45) film of 100 nm thickness is used to coat a glass camera lens (n = 1.56). what wavelength of light in the visible region (390 to 710 nm) will be most efficiently transmitted by this system?

Answer 1

Path difference for clear transmission in the given slab is given by

$2\mu_{1} t = \frac{\lambda}{2} + N\lambda$

here

$2*mu_1*t = \frac{(2N+1)}{2}\lmabda$

given that

$\mu_1 = 1.45$

$\mu_2 = 1.56$

t = 100 nm

now we have

$2*1.45* 100 nm= \frac{2N+1}{2}\lambda$

Now

$\lambda = \frac{580 nm}{2N+1}$

So at N = 0

$\lambda = 580 nm$

so the wavelength in the given range is 580 nm