Find the thickness of a plate which will produce a change in optical path equal to half the wavelength `lamda` of the light passing through it normally. The refractive index of the plate is `mu`.

Explanation

To find the thickness of a plate that produces a change in optical path equal to half the wavelength of light passing through it normally, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the thickness \( t \) of a plate such that the change in optical path \( \Delta x \) is equal to \( \frac{\lambda}{2} \), where \( \lambda \) is the wavelength of the light. The refractive index of the plate is given as \( \mu \).

2. **Write the Optical Path Difference Formula**: The optical path difference \( \Delta x \) when light passes through a medium is given by the formula:
\[ \Delta x = ( \mu - 1 ) t \]
where \( \mu \) is the refractive index of the plate and \( t \) is the thickness of the plate.

3. **Set Up the Equation**: According to the problem, we have:
\[ \Delta x = \frac{\lambda}{2} \]
Therefore, we can set up the equation:
\[ ( \mu - 1 ) t = \frac{\lambda}{2} \]

4. **Rearrange to Solve for Thickness \( t \)**: We can rearrange the equation to solve for \( t \):
\[ t = \frac{\frac{\lambda}{2}}{\mu - 1} \]
Simplifying this gives:
\[ t = \frac{\lambda}{2( \mu - 1 )} \]

5. **Final Expression**: Thus, the thickness \( t \) of the plate that produces a change in optical path equal to half the wavelength of light is given by:
\[ t = \frac{\lambda}{2( \mu - 1 )} \]

### Final Answer:
The thickness of the plate is \( t = \frac{\lambda}{2( \mu - 1 )} \).