Question

An object is placed at a large distance infront of a concave mirror of radius of curvature 40cm.The image will be formed infront of the mirror at a distance of 20cm or 30cm or 40cm or 50cm​

Answer 1

Answer :-

→ Image distance = -20 cm .

To Find :-

→ Image distance .

Explanation :-

Given that radius of curvature (R) = 40cm

hence ,we know that

$\implies \boxed{ \sf{ R = 2F }} \\ \therefore \\ \implies \sf{40 = 2F } \\ \\ \implies \boxed{\sf{ F = -20 \: cm \: }}$

because focal length of a concave mirror is negative .

now ,apply mirror formula

$\implies \boxed{ \sf{\frac{1}{F} = \frac{1}{v} + \frac{1}{u} }}$

here ,object is placed is at large distance ( take infinity )

hence ,

$\implies \: \sf{\frac{1}{-20} = \frac{1}{v} + \frac{1}{ \infty} } \\ \\ \implies \sf{\frac{1}{-20} = \frac{1}{v} + 0 }\: \: \: \: \: \: \: \boxed{\because \infty = \frac{1}{0} } \\ \\ \implies \sf{ \frac{1}{v} = \frac{-1}{20} } \\ \\ \implies \: \boxed{\sf{v = -20 \: cm}}$

hence image formed at -20 cm .means image is on focal length .

because image distance is negative hence image is behind the mirror and virtual.

Answer 2

$\tt{\huge{\orange {Hello!!!!}}} S.D.$

QUESTION :

An object is placed at a large distance infront of a concave mirror of radius of curvature 40cm.

The image will be formed infront of the mirror at a distance of :

A. 20cm √√√√

B. 30cm

C. 40cm

D. 50cm

SOLUTION :

This question is among the easiest questions asked in Optics.

Here , the Object Is placed at Infinity.

We know that for a Concave Mirror, When The Object is At Infinity, The image formed is at the focus.

We know that Focal length = Radial Length / 2 = 40 cm / 2 = 20 cm .

Hence Option A Is Correct...