Radius of curvature of concave mirror is 40 cm and the size of image is twice as that of object, then the object distance is

Question

Radius of curvature of concave mirror is 40 cm and the size of image is twice as that of object, then the object distance is (A) 60 cm (B) 20 cm (C) 40cm (D) 30cm

Tardigrade Admin · Accepted Answer

Given, R=2 f=40 cm. ∴ f=20 cm m=2 m=(v/u)=2 ∴ v=2 u Using mirror formula, (1/f)=(1/v)+(1/u) (1/20)=(1/2 u)+(1/u)=(1+2/2 u) u=30 cm

Q. Radius of curvature of concave mirror is $40 c m$ and the size of image is twice as that of object, then the object distance is

60 cm

20 cm

40cm

30cm

Given, $R = 2 f = 40 c m$ .
$∴ f = 20 c m$
$m = 2 m = \frac{v}{u} = 2$
$∴ v = 2 u$
Using mirror formula,
$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
$\frac{1}{20} = \frac{1}{2 u} + \frac{1}{u} = \frac{1 + 2}{2 u}$
$u = 30 c m$

Q. Radius of curvature of concave mirror is 40cm and the size of image is twice as that of object, then the object distance is