Question

What is the formula for linear magnification for lens?

v = Image distance

u = Object distance

• A. $\frac{u}{v}$
• B. $\frac{v}{u}$
• C. $\frac{-v}{u}$
• D. $\frac{-u}{v}$

Answer 1

The correct option is B

$\frac{v}{u}$

In figure above, In $\Delta AOB$ and $\Delta B^{\prime }{A}^{\prime }O$
$\angle AOB=\angle A^{\prime }O{B}^{\prime }$(alternate interior angles)
and, $\angle ABO=\angle B^{\prime }{A}^{\prime }O$(right angle)
so, $\Delta AOB$ is similar to $\Delta B^{\prime }{A}^{\prime }O$
$\therefore \frac{B^{\prime }{A}^{\prime }}{BA}=\frac{O{B}^{\prime }}{OB}$ ----------- (i)
By sign convention,
B'A' = I (negative)
BA = O (positive)
OB' = v (positive)
OB = u (negative)
$\therefore$ From equation (i)
$\frac{-I}{O}=\frac{v}{-u}Or,\frac{I}{O}=\frac{v}{u}Or,m=\frac{v}{u}$