Question

A spherical mirror forms an erect image three times the size of the object. If the distance between the object and the image is $100cm$ , the nature and the focal length of the mirror is

• A. concave, $\left(37.5\right)cm$
• B. convex, $\left(60\right)cm$
• C. concave, $20cm$
• D. convex, $20cm$

Answer 1

Answer: (A)

concave, $\left(37.5\right)cm$

The size of the image here is three times the size of the object that means the image is magnified, hence the nature of the mirror is concave.

Now let us consider that the image is real in nature, hence

The object distance is $-u$

The image distance is $-v$

As the distance between the image and object is given as $100cm$, therefore if object distance is $u$ then image distance is given as

$v=-\left(100+u\right)$ …… (1)

As the image is erect then the magnification is positive, hence the magnification is given as

$m=\frac{v}{u}$

$3=\frac{-\left(100+u\right)}{-u}$

$u=50cm$

Therefore the object distance is $-50cm$ now image distance can be concluded by substituting the value of $u$ in equation (1),

$v=-\left(100+50\right)=-150cm$

Now the focal length is given as

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

Hence

$\frac{1}{f}=-\frac{1}{50}-\frac{1}{150}$

$\frac{1}{f}=\frac{-4}{150}$

$f=-37.5cm$

Hence the nature of the mirror is concave and the focal length is $37.5cm$.