Question

A small candle, $2.5cm$ in size is placed at $27cm$ in front of a concave mirror of radius of curvature $36cm$. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?

• A. 54 cm
• B. 27 cm
• C. 28 cm
• D. 475 cm

Answer 1

Answer: (A)

Given, radius of curvature of concave mirror, $R=-36m$
(For concave mirror radius of curvature is taken as negative)
$\therefore$ Focal length $f=\frac{R}{2}=\frac{36}{2}=-18cm$
Distance of object $u=-27cm$
(Object distance is always taken as negative)
Height of object $O=2.5cm$
Use the mirror formula
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$
$\Rightarrow -\frac{1}{-18}=\frac{1}{-27}-\frac{1}{54}$
$\frac{1}{v}=-\frac{1}{18}+\frac{1}{27}=\frac{-3+2}{54}=-\frac{1}{54}$
Distance of screen from mirror $v=-54cm$
Let the size of image be $I$.
By using the formula of magnification for mirror
$m=-\frac{v}{u}=\frac{I}{O}$
$\frac{-(-54)}{-27}=\frac{1}{2.5}$
$I=-5cm$
The negative sign shows that the image is formed in front of the mirror and it is inverted.
Thus, the screen should be placed at a distance $54cm$ and the size of image is $5cm$, real, inverted and magnified in nature.