Question

A convex mirror of radius of curvature 30 cm forms an image that is half the size of the object. The object distance is:

• A. −15 cm
• B. 45 cm
• C. −45 cm
• D. 15 cm

Answer 1

Answer: (A)

−15 cm

Answer 2

Step 1: Given Parameters

Radius of curvature $R = 30 \, \text{cm}$. For a mirror, focal length $f = \frac{R}{2} = +15 \, \text{cm}$ (positive for a convex mirror).

Step 2: Use the Magnification Formula for Mirrors

Given that the image is half the size of the object, the magnification $m = \frac{1}{2}$. For a convex mirror, a virtual image is formed for a real object, so $m$ is positive:

$m = +\frac{1}{2}$

Step 3: Apply the Mirror Formula

The magnification formula is $m = \frac{f}{f - u}$. Substitute $m = \frac{1}{2}$ and $f = 15 \, \text{cm}$:

$\frac{1}{2} = \frac{15}{15 - u}$

Step 4: Solve for $u$

$15 - u = 30 \implies u = -15 \, \text{cm}$

So, the correct answer is: -15 cm