Question

The focal length of a thin biconvex lens is `20 cm`. When an object is moved from a distance of `25 cm` in front of it to `50 cm`, the magni-fication of its image changes from `m_(25) to m_(50)`. The ratio `(m_(25))/(m_(50))` is.

Answer 1

Correct Answer - 6

Answer 2

 Given

f = 20 cm 

\(u_1=-25\)

\(u_2=-50\)

when u = -25

\(\frac 1f=\frac 1v-\frac 1u\)

\(\frac 1v=\frac 1f+\frac 1u\)

\(\frac 1v=\frac{1}{20}+\frac{1}{(-25)}\)

\(\frac 1v=\frac{5-4}{100}\)

\(\frac 1v=\frac{1}{100}\)

v = 100 cm

\(m_1=\frac{-v}{u}\Rightarrow \frac{-100}{-25}=4\)

when u = -50

\(\frac 1f=\frac 1v+\frac 1u\)

\(\frac 1V=\frac {1}{20}-\frac{1}{50}\)

\(\frac 1V=\frac{5-2}{100}\)

\(\frac 1V=\frac{3}{100}\)

\(V = \frac{100}{3}\)

\(m_2=\frac{-v}{u}=\frac{\frac{100}{3}}{50}=\frac 23\)

\(\cfrac{m_1}{m_2}=6.\)