On placing a thin film of mica of thickness `12xx10^(-5)cm` in the path of one of the interfering beams in young's double slit experiment using monochromatic light, the fringe pattern shifts through a distance equal to the width of a bright fringe. If `lamda=6xx10^(-5)cm`, the refractive index of mica is

Options

A. 1.33
B. 1.5
C. 2.5
D. 1.4

Explanation

To solve the problem, we need to find the refractive index of mica when a thin film is placed in the path of one of the beams in Young's double slit experiment. The given parameters are:

- Thickness of the mica film, \( t = 12 \times 10^{-5} \) cm
- Wavelength of light, \( \lambda = 6 \times 10^{-5} \) cm

### Step-by-Step Solution:

1. **Understanding the Shift in Fringe Pattern**:
The problem states that the fringe pattern shifts by a distance equal to the width of a bright fringe. The width of a bright fringe in Young's double slit experiment is given by the formula:
\[ \text{Width of bright fringe} = \frac{D \lambda}{d} \]
where \( D \) is the distance from the slits to the screen and \( d \) is the separation between the slits.

2. **Relating Shift to Fringe Width**:
The shift \( s \) caused by introducing a thin film of thickness \( t \) and refractive index \( \mu \) is given by:
\[ s = t (\mu - 1) \frac{D}{d} \]
Since the shift is equal to the width of a bright fringe, we can set these two expressions equal:
\[ t (\mu - 1) \frac{D}{d} = \frac{D \lambda}{d} \]

3. **Canceling Common Terms**:
We can cancel \( \frac{D}{d} \) from both sides (assuming \( D \) and \( d \) are not zero):
\[ t (\mu - 1) = \lambda \]

4. **Rearranging for Refractive Index**:
Now, we can solve for the refractive index \( \mu \):
\[ \mu - 1 = \frac{\lambda}{t} \]
\[ \mu = \frac{\lambda}{t} + 1 \]

5. **Substituting Values**:
Substitute the values of \( \lambda \) and \( t \):
\[ \mu = \frac{6 \times 10^{-5} \text{ cm}}{12 \times 10^{-5} \text{ cm}} + 1 \]

6. **Calculating the Refractive Index**:
\[ \mu = \frac{6}{12} + 1 = 0.5 + 1 = 1.5 \]

7. **Final Answer**:
The refractive index of mica is \( \mu = 1.5 \).