While a moving picture is being screened, a boy introduced a glass slab of thickness 3 cm and refractive index 1.5 between the projector and the screen. In order to have a clear picture on the screen the screen should be moved through a distance of

Options

A. 1 cm away
B. 1 cm nearer
C. 2 cm away
D. 3 cm away

Answer

To solve the problem, we need to determine how far the screen should be moved to maintain a clear picture after introducing a glass slab between the projector and the screen.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Thickness of the glass slab (t) = 3 cm
- Refractive index of the glass slab (μ) = 1.5

2. **Use the Formula for Normal Shift:**
The normal shift (Δx) caused by a glass slab is given by the formula:
\[ \Delta x = t \left(1 - \frac{1}{\mu}\right) \]
where:
- \( t \) is the thickness of the slab,
- \( \mu \) is the refractive index of the slab.

3. **Substitute the Values into the Formula:**
\[ \Delta x = 3 \, \text{cm} \left(1 - \frac{1}{1.5}\right) \]

4. **Calculate the Value Inside the Parenthesis:**
\[ 1 - \frac{1}{1.5} = 1 - \frac{2}{3} = \frac{1}{3} \]

5. **Calculate the Normal Shift:**
\[ \Delta x = 3 \, \text{cm} \times \frac{1}{3} = 1 \, \text{cm} \]

6. **Determine the Direction of Movement:**
Since the glass slab is placed between the projector and the screen, the image will shift towards the glass slab. Therefore, to maintain a clear picture, the screen must be moved towards the projector.

7. **Final Answer:**
The screen should be moved through a distance of **1 cm** towards the projector.