White light is incident on a soap film at an angle of `60^@`. On examining the reflecting light by a spectroscope, a dark band corresponding to wavelength `6200Å` is found. Find the minimum thickness of the film. Take refractive index of film = 1.33.

Explanation

To find the minimum thickness of the soap film that produces a dark band corresponding to the wavelength of 6200 Å when white light is incident at an angle of 60°, we can follow these steps:

### Step 1: Understand the conditions for destructive interference
For a soap film, the condition for destructive interference (dark band) in reflected light is given by:
\[ 2 \mu t \cos r = \lambda \]
where:
- \( \mu \) is the refractive index of the film,
- \( t \) is the thickness of the film,
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