Question

When an object is placed 40 cm away from a spherical mirror an image of magnification $\frac{1}{2}$ is produced. To obtain an image with magnification of $\frac{1}{3}$, the object is to be moved:

• A. 40 cm away from the mirror.
• B. 80 cm away from the mirror.
• C. 20 cm towards the mirror.
• D. 20 cm away from the mirror.

Hint:

Use the magnification formula to find the object distance.

Answer 1

The Correct Option is A

1. Given: - Object distance, $u = -40 \mathrm{~cm}$ - Magnification, $m = \frac{1}{2}$
2. Magnification formula: $m = \frac{f}{f - u}$ Substituting the given values: $\frac{1}{2} = \frac{f}{f - (-40)}$ Solving for focal length $f$: $f + 40 = 2f \implies f = 40 \mathrm{~cm}$
3. For a magnification of $\frac{1}{3}$ with $f = 40 \mathrm{~cm}$: $\frac{1}{3} = \frac{40}{40 - u}$ Solving for object distance $u$: $40 - u = 120 \implies u = -80 \mathrm{~cm}$Therefore, the correct answer is (1) 40 cm away from the mirror.