The diagram shows a mirror system. If after two reflections the image and the object O coincide with each other, then the value of radius of curvature (in metre) of the concave mirror is (Take a=3 m )

Question

The diagram shows a mirror system. If after two reflections the image and the object O coincide with each other, then the value of radius of curvature (in metre) of the concave mirror is (Take a=3 m ) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

For the image to coincide with object, image formed by concave mirror must be at a in front of plane mirror. ∴ (1/v)+(1/u)=(1/f) ⇒ (1/-2 a)+(1/-4 a)=(1/f) ⇒ f=-4 m ∴ R=8 m

Q. The diagram shows a mirror system. If after two reflections the image and the object $O$ coincide with each other, then the value of radius of curvature (in metre) of the concave mirror is (Take $a = 3 m$ )

For the image to coincide with object, image formed by concave mirror must be at $a$ in front of plane mirror.
$∴ \frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
$\Rightarrow \frac{1}{- 2 a} + \frac{1}{- 4 a} = \frac{1}{f}$
$\Rightarrow f = - 4 m$
$∴ R = 8 m$

Q. The diagram shows a mirror system. If after two reflections the image and the object O coincide with each other, then the value of radius of curvature (in metre) of the concave mirror is (Take a=3m )

For the image to coincide with object, image formed by concave mirror must be at a in front of plane mirror. ∴v1​+u1​=f1​ ⇒−2a1​+−4a1​=f1​ ⇒f=−4m ∴R=8m

Q. The diagram shows a mirror system. If after two reflections the image and the object $O$ coincide with each other, then the value of radius of curvature (in metre) of the concave mirror is (Take $a = 3 m$ )

For the image to coincide with object, image formed by concave mirror must be at $a$ in front of plane mirror.
$∴ \frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
$\Rightarrow \frac{1}{- 2 a} + \frac{1}{- 4 a} = \frac{1}{f}$
$\Rightarrow f = - 4 m$
$∴ R = 8 m$