Question

An object is placed Infront of a plane mirror 12 cm away from it. The object is kept fixed while the plane mirror is shifted towards the object by a distance of 4 cm. The length of shift in the position of image is equal to ___________ cm.

Answer 1

Correct Answer: 8

Step 1: Initial Distance Between Object and Image

For a plane mirror, the image is formed at the same distance behind the mirror as the object is in front of it.

Initially, the object is placed \( 12 \, \text{cm} \) away from the mirror. Therefore, the distance between the object and the image is:

\[ \text{Distance} = 2 \times 12 = 24 \, \text{cm} \]

Step 2: Final Distance After Shifting the Mirror

The mirror is shifted towards the object by \( 4 \, \text{cm} \), so the new distance between the object and the mirror becomes:

\[ 12 - 4 = 8 \, \text{cm} \]

Therefore, the distance between the object and the image is:

\[ \text{Distance} = 2 \times 8 = 16 \, \text{cm} \]

Step 3: Calculate the Shift in the Image Position

The shift in the image position is the difference between the initial and final distances between the object and the image:

\[ \text{Shift} = 24 - 16 = 8 \, \text{cm} \]

Conclusion:

The shift in the position of the image is 8 cm.

Answer: 8 cm

Answer 2