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  • A 10 mm long awl pin is placed vertically in front of a concave mirror. A 5 mm long image of the awl pin is formed at 30 cm in front of the mirror. The focal length of this mirror is (a) – 30 cm (b) – 20 cm (c) – 40 cm (d) – 60 cm

A 10 mm long awl pin is placed vertically in front of a concave mirror. A 5 mm long image of the awl pin is formed at 30 cm in front of the mirror. The focal length of this mirror is

(a) – 30 cm

(b) – 20 cm

(c) – 40 cm

(d) – 60 cm

Answers (1)

Answer : B

Given,

Size of object, O = + 10.0 mm = + 1.0 cm

Size of image size, I = 5.0 mm = 0.5 cm

Image distance = − 30 cm (as image is real)

Let, object distance = u

Focal length= f

Magnification m = \frac{I}{O}

Magnification is also given as,m=-\frac{v}{u}

Therefore, \frac{I}{O}=\frac{-v}{u}

\frac{0.5}{1.0}=-\frac{30}{u}

Therefore, u=-60\; cm

Focal length is given by \frac{1}{f}=\left ( \frac{1}{v} \right )+\left ( \frac{1}{u} \right )

or, \frac{1}{f}=-\frac{3}{60}

Therefore, f= -20\; cm

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