Question

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

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