A thin mica sheet of thickness `2xx10^-6m` and refractive index `(mu=1.5)` is introduced in the path of the first wave. The wavelength of the wave used is `5000Å`. The central bright maximum will shift

Options

A. two fringes upward
B. two fringes downward
C. ten fringes upward
D. None of these

Explanation

To solve the problem of finding the shift in the central bright maximum when a thin mica sheet is introduced, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Thickness of the mica sheet, \( t = 2 \times 10^{-6} \, \text{m} \)
- Refractive index of the mica sheet, \( \mu = 1.5 \)
- Wavelength of the wave, \( \lambda = 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} \)

2. **Understand the Concept of Fringe Shift:**
- When a thin film (like the mica sheet) is introduced in the path of one of the waves in an interference pattern, it causes a shift in the interference fringes.
- The formula for the fringe shift (in terms of the number of fringes shifted) is given by:
\[ \text{Shift} = \frac{t (\mu - 1)}{\lambda} \]
- Here, \( t \) is the thickness of the film, \( \mu \) is the refractive index, and \( \lambda \) is the wavelength of the light used.

3. **Substitute the Values into the Formula:**
- Substitute the given values into the formula:
\[ \text{Shift} = \frac{(2 \times 10^{-6}) \times (1.5 - 1)}{5000 \times 10^{-10}} \]
- Simplifying the expression:
\[ \text{Shift} = \frac{(2 \times 10^{-6}) \times (0.5)}{5000 \times 10^{-10}} = \frac{1 \times 10^{-6}}{5000 \times 10^{-10}} \]

4. **Calculate the Shift:**
- Calculate the denominator:
\[ 5000 \times 10^{-10} = 5 \times 10^{-7} \]
- Now, calculate the shift:
\[ \text{Shift} = \frac{1 \times 10^{-6}}{5 \times 10^{-7}} = 2 \]

5. **Interpret the Result:**
- The result indicates that the central bright maximum shifts by 2 fringes upward.

### Final Answer:
The central bright maximum will shift **2 fringes upward**.

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