A little candle, 4.5 cm in size is located at 30 cm in front of a concave mirror of radius of curvature 42 cm. find the distance from the mirror should a screen be located in order to obtain a sharp image?

Question

Question

This question was previously asked in

AAI ATC Junior Executive 25 March 2021 Official Paper (Shift 1)

Answer 1

Concept:

Using mirror formula:

\(\frac{1}{v}+ \frac{1}{u} = \frac{1}{f}\)

Calculation:

Given u = -30cm , f = - R/2 = - 42/2 = - 21cm,

\(\frac{1}{v} + \frac{1}{-30} = \frac{1}{-21}\)

\(\frac{1}{v} = \frac{21-30}{30\times 21}\)
\(\frac{1}{v} = \frac{1}{-70}\)

\(v = -70cm \)

Hence the screen should be placed 70cm in front of the mirror in order to obtain a sharp image.

Hint

The focal length for a concave mirror is negative because all the parallel rays reflecting from the mirror surface converge in front of the mirror and for a convex mirror focal length is positive because parallel rays converge inside the mirror virtually
Conventionally left side of the mirror is taken is the negative and the right side is taken as positive, where parallel rays come from the left side.