Question

Lenses of power $3\, D$ and $-5\,D $ are combined to form a compound lens. An object is placed at a distance of $50\, cm$ 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
$\therefore P=P_{1}+P_{2}$
$\therefore P=3 D+(-5 D)=-2 D$
Also power $=\frac{1}{f_{(\text {metres })}}$ diopters
$\therefore f=\frac{100}{P}=-\frac{100}{2} \,m$
$=-50\, m$
From lens formula
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
Putting $f=-50\, cm , u=-50\, cm$
$-\frac{1}{50}=\frac{1}{v}-\left(-\frac{1}{50}\right)$
$\Rightarrow v=-25 \,cm$
Hence, image is formed at same side as object.
Note: Since, focal length is negative, it is a diverging lens.