Light of wavelength 6000Å is incident on a thin glass plate of refractive index 1.5 such that angle of refraction into the plate is `60^(@)`. Calculate the smallest thickness of plate which will make it appear dark by reflection.

Explanation

To solve the problem, we need to find the smallest thickness of a thin glass plate that will make it appear dark by reflection when light of wavelength 6000 Å is incident on it. The angle of refraction into the plate is given as 60 degrees, and the refractive index of the glass is 1.5.

### Step-by-Step Solution:

1. **Understand the Condition for Darkness**:
For destructive interference (dark fringe) in reflected light, the path difference must be equal to an odd multiple of half wavelengths. The condition for dark fringes can be expressed as:
\[
2 \mu t \cos r = (n + \frac{1}{2}) \lambda
...