An object is 8 cm high. It is desired to form a real image 4 cm high at 60 cm from the mirror. The type of mirror needed with the focal length is

Question

An object is 8 cm high. It is desired to form a real image 4 cm high at 60 cm from the mirror. The type of mirror needed with the focal length is (A) convex mirror with focal length f=40 cm (B) convex mirror with focal length f=20 cm (C) concave mirror with focal length f=-40 cm (D) concave mirror with focal length f=-20 cm

Tardigrade Admin · Accepted Answer

M=(I/O)=(v/u) Given, O=8 cm, I=4 cm, v=60 cm ∴ (4/8)=(60/u) ⇒ s u=120 cm (1/f)=(1/v)+(1/u)=(1/60)+(1/120) ⇒ s t=40 cm (convex)

Q. An object is $8 c m$ high. It is desired to form a real image $4 c m$ high at $60 c m$ from the mirror. The type of mirror needed with the focal length is

convex mirror with focal length f=40 cm

convex mirror with focal length f=20 cm

concave mirror with focal length f=-40 cm

concave mirror with focal length f=-20 cm

$M = \frac{I}{O} = \frac{v}{u}$
Given, $O = 8 c m, I = 4 c m, v = 60 c m$
$∴ \frac{4}{8} = \frac{60}{u}$
$\Rightarrow s u = 120 c m$
$\frac{1}{f} = \frac{1}{v} + \frac{1}{u} = \frac{1}{60} + \frac{1}{120}$
$\Rightarrow s t = 40 c m$ (convex)

Q. An object is 8cm high. It is desired to form a real image 4cm high at 60cm from the mirror. The type of mirror needed with the focal length is