An object of size 7 cm is placed 27 cm in front of a concave mirror of a focal length of 18 cm. At what distance from the mirror should a screen be placed so that a sharp, focused image can be obtained?

An object of size

7 cm

is placed

27 cm

in front of a concave mirror of a focal length of

18 cm

. The screen can be placed

54 cm

to the left of the mirror so that a sharp, focused image can be obtained.
Given,
Object distance,

(u) = - 27 cm

Focal length,

(f) = - 18 cm

Object height,

(h) = 7 cm

Applying mirror formula,

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

By substituting given values, we get

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

\Rightarrow

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

\Rightarrow

\frac{1}{v} = \frac{2 - 3}{54}

\Rightarrow

v = - 54 cm

-ve sign indicates that the image forms in the front of the concave mirror and on the same side of the object.

An object of size $7 cm$ is placed $27 cm$ in front of a concave mirror of a focal length of $18 cm$ . At what distance from the mirror should a screen be placed so that a sharp, focused image can be obtained?