Question

The size of the image of an object, which is at infinity, as formed by a convex lens of focal length $30\, cm$ is $2 \, cm .$ If a concave lens of focal length $20 \, cm$ is placed between the convex lens and the image at a distance of $26\, cm$ from the lens, the new size of the image is :

• A. 1.25 cm
• B. 2.5 cm
• C. 1.05 cm
• D. 2 cm

Answer 1

Answer: (B)

$A 'B'$ is the real image due to convex lens and it is at Focus of convex lens.
$A'B'$ acts as virtual object for concave lens and object distance is $+4 \,cm$
$\frac{1}{f} =\frac{1}{v}-\frac{1}{u} v=\frac{20}{4} $
$\frac{1}{v} =\frac{1}{f}+\frac{1}{u} v=5 \,cm$
$\frac{1}{v} =\frac{1}{-20}+\frac{1}{4} $
$\frac{1}{v} =\frac{-1+5}{20}=\frac{4}{20} $
$m =\frac{h_{i}}{h_{o}}=\frac{v}{u} $
$h_{i} =\frac{v h_{o}}{u} $
$=\frac{5 \times 2}{4}=\frac{10}{4}=2.5\, cm$