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) 15 cm in front of the mirror (b) 30 cm in front of the mirror (c) between 15 cm and 30 cm in front of the mirror more than 30 cm in front of the mirror.

• Soln:

Answer is (d) more than 30 cm in front of the mirror

Explanation:

Here f= 15,

Radius of curvature is double the focal length hence c=30

When object is placed on c, its image is of the same size, inverted and is formed on c.

Let’s go step by step and make the concept very clear.

1. What does “rays from the Sun” mean?

The Sun is very far away from the Earth, so the light rays from it are parallel when they reach a mirror.

For a concave mirror, parallel rays always:

converge (meet) at the focus (F)

You are told that these rays meet 15 cm in front of the mirror, so:

• Focal length (f) = 15 cm

2. Important mirror points

For a concave mirror:

• Focus (F) = ( f = 15 cm} )
• Centre of curvature (C) = ( 2f )

C = 2f

So, C = 2 \times 15 = 30 cm}

3. When is image equal to object?

In a concave mirror:

• If the object is placed at centre of curvature (C):
  • Image is formed at C
  • Image is same size as the object
  • Image is real and inverted

This is a standard result in ray diagrams.

4. Why does this happen?

At ( C = 2f ):

• Rays reflect symmetrically
• The image distance = object distance
• Magnification ( m = 1 )

So,
Image size = Object size

5. Final Answer

The object must be placed at 30 cm in front of the mirror

✔️ Correct option: (b) 30 cm in front of the mirror