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MHT CET · Physics · Ray Optics

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. A \(2\mathrm{f}\)
  2. B \(5 \mathrm{f}\)
  3. C \(4 \mathrm{f}\)
  4. D \(3 \mathrm{f}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(5 \mathrm{f}\)

Step-by-step Solution

Detailed explanation

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, \(\frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}}\)
\(
\begin{aligned}
& -\frac{4}{u}-\frac{1}{u}=\frac{1}{f} \\
& u=-5 f
\end{aligned}
\)