What is the thinnest film of coating with n= 1.42 on glass (n=1.52) for which destructive interference of the red component (650 nm) of an incident white light beam in air can take place by reflection ?

Explanation

To find the thinnest film of coating with a refractive index \( n = 1.42 \) on glass (with \( n = 1.52 \)) for which destructive interference of the red component (650 nm) of an incident white light beam in air can take place by reflection, we can follow these steps:

### Step 1: Understand the condition for destructive interference
For destructive interference to occur in thin films, the path difference between the light waves reflected from the top and bottom surfaces of the film must be given by the formula:
\[ \text{Path difference} = (2n - 1) \frac{\lambda}{2} \]
where \( n \) is the refractive index of the film and \( \lambda \) is the wavelength of light in vacuum (or air).
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