Question

The graph shows how the magnification m produced by a thin lens varies with image distance v. What is the focal length of the lens used ?

• A. $\frac{b^{2}c}{a}$
• B. $\frac{b^2}{ac}$
• C. $\frac{a}{c}$
• D. $\frac{b}{c}$

Answer 1

The correct option is D $\frac{b}{c}$

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$1-\frac{v}{u}=\frac{v}{f}$
$1-m=\frac{v}{f}$
$m=1-\frac{v}{f}$
At $v=a,m_1=1-\frac{a}{f}$
At $v=a+b,m_2=1-\frac{a+b}{f}$
$m_2-m_1=c=[1-\frac{a+b}{f}]-[1-\frac{a}{f}]$
$c=\frac{b}{f}$
$f=\frac{b}{c}$