Question

In fig., a real image of a point objert O is formed, Which of the following statements is true about each of the arrangements?

1. The object is at the principle focus of the lens.
2. The focal length of the lens is 17 cm.
3. If the mirror is moved so that it is 6 cm from the lens image will also move.

Options

• (i) alone

• (ii) alone

• (i) and (ii) only

• (ii) and (iii) only

• (i), (ii) and (iii)

Answer 1

(i) and (ii) only

Explanation:

From the figure:

• Distance between object \(O\) and mirror \(= 20\,\text{cm}\)
• Distance between lens and mirror \(= 3\,\text{cm}\)

Therefore, distance between object and lens is:

\[ 20-3=17\,\text{cm} \]

Since the rays after passing through the lens become parallel and are reflected back by the plane mirror, the object must be at the principal focus of the convex lens.

Hence,

\[ f=17\,\text{cm} \]

So statements (i) and (ii) are correct.

If the mirror is moved farther away, the parallel rays are still reflected back parallel to themselves and the lens again focuses them at the same point \(O\). Therefore, the image does not move.