If d actual thickness of a plate of refractive index `mu`, then decrease in its thickness due to refraction of light will be

Options

A. `d(mu-1)`
B. `d/mu`
C. `d(1-1/mu)`
D. `d/((mu-1))`

Answer

To solve the problem of finding the decrease in thickness of a plate due to the refraction of light, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Let the actual thickness of the plate be \( D \).
- Let the refractive index of the plate be \( \mu \).

2. **Understand Apparent Depth**:
- When light passes through the plate, it refracts, and the depth appears to be less than the actual thickness. This is referred to as the apparent depth.
- The formula for apparent depth (\( d' \)) is given by:
\[ d' = \frac{D}{\mu} \]

3. **Calculate the Decrease in Thickness**:
- The decrease in thickness due to refraction can be calculated by finding the difference between the actual thickness and the apparent depth:
\[ \text{Decrease in thickness} = D - d' \]
- Substituting the value of \( d' \):
\[ \text{Decrease in thickness} = D - \frac{D}{\mu} \]

4. **Factor Out \( D \)**:
- To simplify the expression, factor out \( D \):
\[ \text{Decrease in thickness} = D \left(1 - \frac{1}{\mu}\right) \]

5. **Final Expression**:
- The final expression for the decrease in thickness due to refraction is:
\[ \text{Decrease in thickness} = D \left(1 - \frac{1}{\mu}\right) \]

### Conclusion:
The decrease in thickness of the plate due to the refraction of light is given by:
\[ D \left(1 - \frac{1}{\mu}\right) \]