A double slit experiment is performed with light of wavelength `500nm`. A thin film of thickness `2mum` and refractive index `1.5` is introduced in the path of the upper beam. The location of the central maximum will

Options

A. remain unshined
B. shift downward by nearly two fringes
C. shift upward by nearly two fringes
D. shift downwards by ten fringes.

Answer

To solve the problem, we will determine the fringe shift caused by the introduction of a thin film in the path of one of the beams in a double slit experiment. Here are the steps to find the location of the central maximum after the introduction of the thin film.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Wavelength of light, \( \lambda = 500 \, \text{nm} = 500 \times 10^{-9} \, \text{m} \)
- Thickness of the thin film, \( t = 2 \, \mu m = 2 \times 10^{-6} \, \text{m} \)
- Refractive index of the thin film, \( \mu = 1.5 \)

2. **Calculate the Fringe Shift:**
The formula for fringe shift \( n \) due to a thin film of refractive index \( \mu \) and thickness \( t \) is given by:
\[ n = \frac{(\mu - 1) \cdot t}{\lambda} \]
Substituting the values:
\[ n = \frac{(1.5 - 1) \cdot (2 \times 10^{-6})}{500 \times 10^{-9}} \]

3. **Simplify the Calculation:**
\[ n = \frac{0.5 \cdot (2 \times 10^{-6})}{500 \times 10^{-9}} = \frac{1 \times 10^{-6}}{500 \times 10^{-9}} = \frac{1}{0.5} = 2 \]

4. **Interpret the Result:**
The fringe shift \( n = 2 \) indicates that the central maximum will shift by 2 fringe widths due to the introduction of the thin film.

5. **Determine the New Position of the Central Maximum:**
Since the central maximum shifts by 2 fringes, the new position of the central maximum will be at the position of the 2nd order maximum on the screen.

### Conclusion:
The location of the central maximum will shift to the position of the 2nd order maximum due to the introduction of the thin film.