Question

A biconvex lens has a radius of curvature of magnitude $20\, cm$. Which one of the following options describe best the image formed of an object of height $2 \,cm$ placed $30\, cm$ from the lens?

• A. Virtual, upright, height = 1 cm
• B. Virtual, upright, height = 0.5 cm
• C. Real, inverted, height = 4 cm
• D. Real, inverted, height = 1 cm

Answer 1

Answer: (C)

Real, inverted, height = 4 cm

Answer 2

Focal length of the lens
$\frac{1}{ f }=(1.5-1)\left(\frac{1}{20}-\frac{1}{-20}\right)=\frac{1}{20}$
$f =20 \,cm$
From lens formula
$\frac{1}{ v }-\frac{1}{ u }=\frac{1}{ f }$
$\frac{1}{ v }-\frac{1}{-30}=\frac{1}{20}$
$v =60\, cm$
$\frac{ I }{ O }= m =\frac{ v }{ u }=\frac{60}{-30}=- I$
$I =-2(0)=-2 \times 2=-4 cm$
so image will be real inverted and of size $4\, cm$.