Question

In the experiment of a convex lens, if the distance between the object and its real image is 90 cm and the magnification produced by the lens is 2, then the focal length of the convex lens is

• A. 40 cm
• B. 15 cm
• C. 30 cm
• D. 20 cm

Hint:

- Always write both lens formula and magnification formula. - For real images, $v>0$; for virtual images, $v<0$. - If object-image distance given, express one variable in terms of the other using magnification.

Answer 1

The Correct Option is C

1. Lens formula: $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$, magnification $m = v/u$ (real image: $v>0$).
2. Given: $v - u = 90~\text{cm}$, $m = v/u = 2 \implies v = 2u$.
3. Distance equation: $v - u = 2u - u = u = 30~\text{cm}$ → object distance $u = 30$ cm, $v = 60$ cm.
4. Focal length: $1/f = 1/60 - 1/30 = -1/60 \implies f = 30~\text{cm}$.