A thin mica sheet of thickness `4xx10^(-6)` m and refractive index `(mu=1.5)` is introduced in the path of the light from upper slit. The wavelength of the wave used is `5000 Å` The central bright maximum will shift

Options

A. 4 fringes upward
B. 2 fringes downward
C. 10 fringes upward
D. None of these

Explanation

To solve the problem of the central bright maximum shifting due to the introduction of a thin mica sheet, we will follow these steps:

### Step 1: Understand the Parameters
We are given:
- Thickness of the mica sheet, \( T = 4 \times 10^{-6} \) m
- Refractive index of mica, \( \mu = 1.5 \)
- Wavelength of light, \( \lambda = 5000 \) Å = \( 5000 \times 10^{-10} \) m = \( 5 \times 10^{-7} \) m

### Step 2: Calculate the Fringe Shift
The formula for fringe shift when a thin film is introduced is given by:
\[ \text{Fringe Shift} = \frac{T}{\lambda} (\mu - 1) \]

### Step 3: Substitute the Values
Substituting the values into the formula:
\[ \text{Fringe Shift} = \frac{4 \times 10^{-6}}{5 \times 10^{-7}} (1.5 - 1) \]

### Step 4: Simplify the Expression
Calculating \( \mu - 1 \):
\[ \mu - 1 = 1.5 - 1 = 0.5 \]
Now substituting this back into the fringe shift equation:
\[ \text{Fringe Shift} = \frac{4 \times 10^{-6}}{5 \times 10^{-7}} \times 0.5 \]

### Step 5: Calculate the Fraction
Calculating \( \frac{4 \times 10^{-6}}{5 \times 10^{-7}} \):
\[ \frac{4}{5} \times 10^{1} = 0.8 \times 10^{1} = 8 \]
Thus,
\[ \text{Fringe Shift} = 8 \times 0.5 = 4 \]

### Step 6: Conclusion
The central bright maximum will shift by 4 fringes upward.

### Final Answer
The central bright maximum will shift **4 fringes upward**.

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