Question

A small candle 2.5 cm in size is placed 27 cm in front of a concave mirror of radius of curvature 36 cm.

• A. The distance from the mirror, should a screen be placed in order to receive a sharp image is-54 cm.
• B. The nature of image is virtual inverted w.r.t. object.
• C. The image formed is 8 times highest the object.
• D. The image formed is 3 times highest the object.

Answer 1

The correct option is A The distance from the mirror, should a screen be placed in order to receive a sharp image is-54 cm.

Given,

The object distance is $u=-27cm$

The radius of curvature $R=-36cm$

Hence the focal length is $f=\frac{R}{2}=\frac{-36}{2}=-18cm$

Now to obtain the image distance, substitute the values $f$ and $u$ in the mirror formula

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

$\frac{1}{v}=\frac{1}{u}-\frac{1}{f}$

$\frac{1}{v}=\frac{1}{-18}+\frac{1}{27}$

$\frac{1}{v}=-\frac{1}{54}$

Therefore,

$v=-54cm$

Hence the screen has to be placed at $54cm$ from the mirror to get a sharp image of $-54cm$ .