Question

A point-like object is placed at a distance of $1m$ in front of a convex lens of the focal length of$0.5m$. A plane mirror is placed at a distance of $2m$ behind the lens. The position and nature of the final image formed by the system are:

• A. $1m$ from the mirror, virtual
• B. $2.6m$ from the mirror, virtual
• C. $1m$ from the mirror, real
• D. $2.6m$ from the mirror, real

Answer 1

The correct option is D

$2.6m$ from the mirror, real

Step 1: Given data and draw the diagram of the situation:

The focal length of a convex lens, $f=0.5m$

Distance between plane mirror and lens$=2m$

Distance between the point-like object and convex lens, $u_1=-1m$

Step 2: Find the distance of the image for refraction through a convex lens.

Applying the lens formula, we get

$$\begin{gathered} \frac{1}{v}-\frac{1}{u}=\frac{1}{f} \\ \frac{1}{v}-\frac{1}{(-1)}=\frac{1}{0.5} \\ \frac{1}{v}=1 \\ v=1m \end{gathered}$$

Step 3: Find the position and nature of the final image formed by the system
The image formed by the convex lens will work as the object for the plane mirror and

For the plane mirror, the distance of the object from the mirror$=$distance of the image from the mirror,

Therefore, for the third refraction $u=–3m$

$$\begin{gathered} (1/v)+(1/3)=2/1 \\ V=3/5 \\ =0.6m \end{gathered}$$

So, from the mirror, a distance of the image$=2+0.6$

$=2.6m$

Here, the image will form $2.6m$ away from the mirror and it will be real because it will form on the opposite side from the virtual object.

Hence, option (D) is correct.