A point object is placed in front of a concave mirror. And its image is found to coincide with its own position. Now a glass slab of thickness 15 cm and refractive index 1.5 is placed in between object and the mirror. In order to form image again at the location of object, it is required to move the object

Options

A. towards the mirror by 5 cm
B. away from the mirror by 5 cm
C. towards the mirror by 7.5 cm
D. away from mirror by 7.5 cm

Explanation

To solve the problem, we need to determine how much the point object should be moved in order to form the image at the original position after placing a glass slab between the object and the concave mirror.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- A point object is placed in front of a concave mirror, and its image coincides with its position. This means the object is at the center of curvature (C) of the mirror.
- A glass slab of thickness \( t = 15 \) cm and refractive index \( n = 1.5 \) is placed between the object and the mirror.

2. **Calculate the Shift Due to the Glass Slab**:
- The formula for the lateral shift \( \Delta x \) caused by a slab is given by:
\[ \Delta x = t \left(1 - \frac{1}{n}\right) \]
- Substituting the values:
\[ \Delta x = 15 \left(1 - \frac{1}{1.5}\right) \]
- Calculate \( 1 - \frac{1}{1.5} \):
\[ 1 - \frac{1}{1.5} = 1 - \frac{2}{3} = \frac{1}{3} \]
- Now substitute this back into the formula:
\[ \Delta x = 15 \times \frac{1}{3} = 5 \text{ cm} \]
- Thus, the image shifts by \( 5 \) cm due to the glass slab.

3. **Determine the Required Movement of the Object**:
- To bring the image back to the original position (where the object was initially located), the object must be moved away from the mirror by the same distance that the image has shifted.
- Therefore, the object should be moved \( 5 \) cm away from the mirror.

### Conclusion:
The object should be moved \( 5 \) cm away from the mirror to ensure that the image coincides with the original position of the object after placing the glass slab.