Question

Rays from Sun converge at a point 15 cm in front of a concave mirror. Where should an object be placed so that size of its image is equal to the size of the object?

• A. $15cm$ in front of the mirror
• B. $30cm$ in front of the mirror
• C. between $15cm$ and $30cm$ in front of the mirror
• D. more than $30cm$ in front of the mirror

Answer 1

The correct option is B

$30cm$ in front of the mirror

Step 1: Given information:

Rays from sun $=15cm$

The given mirror is concave mirror

We have to find the size of the object.

Step 2. Concept to be used

The relation between focal length $\left(\mathrm{f}\right)$ and radius of curvature $\left(\mathrm{R}\right)$ of a spherical mirror is that the focal length is equal to half of the radius of curvature.

So,

$\mathrm{f}=\frac{\mathrm{R}}{2}$

Step 3: Find the size of image

The above image represents the given situation.

So, in the case of a concave mirror, the image size becomes equal to the object size when the object distance equals the radius of curvature.

So, the focal length is twice.

Therefore, the image must be formed at

$\mathrm{R}=2\mathrm{f}$

$=2\times 15$

$=30\mathrm{cm}$

Thus, the object is placed at a distance of $30cm$ in front of the mirror.

Hence, option B is the correct answer.