Question

If 25 cm each is the object and image distances due to convex lens, then its focal length is

• A. 50 cm
• B. 25 cm
• C. 15 cm
• D. 12.5 cm

Answer 1

The Correct Option is D

We are given that the object distance $u = 25$ cm and the image distance $v = 25$ cm. 

The lens formula: $$ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} $$ 

Since the lens is convex and forms a real image, the object distance $u$ is taken as negative. 

So $u = -25$ cm. Substituting the given values, we have $$ \frac{1}{f} = \frac{1}{25} - \frac{1}{-25} = \frac{1}{25} + \frac{1}{25} = \frac{2}{25} $$

Therefore, $$ f = \frac{25}{2} = 12.5 \text{ cm} $$ 

The focal length of the convex lens is 12.5 cm.