Question

Lenses of power $3D$ and $-5D$ are combined to form a compound lens. An object is placed at a distance of $50cm$ from this lens. Its image will be formed at a distance from the lens, will be

• A. 25 cm
• B. 20 cm
• C. 30 cm
• D. 40 cm

Answer 1

Answer: (A)

Key Idea: For an achrometic combination powers are additive in nature.
When two lenses of different powers are combined, the power of combination is sum of individual powers
$\therefore P=P_1+P_2$
$\therefore P=3D+(-5D)=-2D$
Also power $=\frac{1}{f_{(\text{metres })}}$ diopters
$\therefore f=\frac{100}{P}=-\frac{100}{2}m$
$=-50m$
From lens formula
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
Putting $f=-50cm,u=-50cm$
$-\frac{1}{50}=\frac{1}{v}-\left(-\frac{1}{50}\right)$
$\Rightarrow v=-25cm$
Hence, image is formed at same side as object.
Note: Since, focal length is negative, it is a diverging lens.