Question

An object S is placed at a distance of 20 cm from a convex lens of focal length 15 cm as shown in the figure. Where should a convex mirror of focal length 25 cm be placed from the lens, so that a real image is formed on the object itself?

• A. 20 cm
• B. 10 cm
• C. 40 cm
• D. 25 cm

Answer 1

The correct option is B 10 cm

To find the image on the object itself, the mirror should be placed such that the ray incident on the mirror should be reflected back on the same path as shown in the figure.
To meet this condition, OI should be the radius of curvature of the mirror.
That is, OI = 2 × f′ = 2 × 25 = 50 cm.

Let x be the distance of the convex mirror from the lens.
For convex lens,
u = –20 cm, f = 15 cm, v = (x + 50) cm
According to the lens formula,
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$$\Rightarrow \frac{1}{x+50}-\frac{1}{(-20)}=\frac{1}{15}$$\Rightarrow x=10cm$
Hence, the correct answer is option (b).