Question

A convex lens has a focal length of 10 cm. Find the location and nature of the image if a point object is placed on the principal axis at a distance of

(a) 9.8 cm

(b) 10.2 cm from the lens.

Answer 1

(a) f = 10 cm; u = 9.8

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}=\frac{1}{f}+\frac{1}{u}=\frac{1}{10}-\frac{1}{9.8}$

$\frac{1}{v}=\frac{9.8-10}{98}=\frac{-0.2}{98}$

$v=-98\times 5$

$=-490\text{cm}$

(same side of object)

$v=490\text{cm}$ on the side of object, (virtual)

(b) u = 10.2

$\frac{1}{v}=\frac{1}{10}-\frac{1}{10.2}$

$=\frac{10.2-10}{102}=\frac{0.2}{102}$

$v=102\times 5=510\text{cm}$ (real)

(opposite side of object)