A convex lens $\mathrm{T}$ is used to form an image whose size is one fourth that of size of object. Then…

A convex lens $\mathrm{T}$ is used to form an image whose size is one fourth that of size of object. Then the object distance is
  1. $2\mathrm{f}$
  2. $5 \mathrm{f}$
  3. $4 \mathrm{f}$
  4. $3 \mathrm{f}$

Solution

Magnification, $\mathrm{m}=-\frac{1}{4}$ (Since the image is real and inverted, it is taken as negative) $\begin{aligned} & \therefore \mathrm{m}=\frac{\mathrm{v}}{\mathrm{u}}=-\frac{1}{4} \\ & \mathrm{v}=-\frac{\mathrm{u}}{4} \end{aligned}$ Lens formula, $\frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}}$ $\begin{aligned} & -\frac{4}{u}-\frac{1}{u}=\frac{1}{f} \\ & u=-5 f \end{aligned}$ *

Asked in: MHT CET 2021 (20 Sep Shift 1)

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