What is the first equation? I have only one chance left Sometimes a non-reflecti

Question

What is the first equation?

I have only one chance left

Sometimes a non-reflective coating Is applied to a lens, such as a camera lens. The coating has an index of refraction between the index of air and the Index of the lens. The coating cancels the reflections of one particular wavelength of the incident light. Usually, it cancels green-yellow light (lambda = 554.0 nm) in the middle of the visible spectrum. (a) Assuming the light is incident perpendicular to the lens surface, what is the minimum thickness of the coating in terms of the wavelength of light in that coating? (Use the following as necessary: lambda.) w = lambda/4 eta (b) If the coating's index of refraction is 1.37, what should be the minimum thickness of the coating? 101.09e-9m

Explanation / Answer

a) We want to choose the film thickness such that destructive interference occurs between the light reflected from the air-film interface (call it wave 1) and from the film-lens interface (call it wave 2). For destructive interference to occur, the phase difference between the two waves must be an odd multiple of half-wavelengths.

The path difference between the front reflection and the back reflection must be half a wavelength, so the "reflected" waves destructively interfere and therefore don't reflect.

2t = film/2, t = thickness of film

The wavelength in the film is :   film = air/n   ---(1)

Hence, the thickness should be,   t = film/4 ---(2)

n = refractive index of film

film = light wavelength in film

air = light wavelength in vacuum (air)

b) Using eqns 1 and 2,

film = 554 nm/1.37 = 404.37 nm  

t = 404.37 nm /4

t = 101.09 * 10-9m

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