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JIPMER 2016
Exam
JIPMER
Year
2016
Subject
Physics
Chapter
Ray Optics

JIPMER 2016 · Physics · Ray Optics

A square wire of side 2.0 cm is placed 20 cm in front of a concave...

A square wire of side 2.0 cm is placed 20 cm in front of a concave mirror of focal length 10 cm with its centre on the axis of the mirror and its plane normal to the axis. The area enclosed by the image of wire is

Options

  1. A7.5 cm27.5 \mathrm{~cm}^2
  2. B6 cm26 \mathrm{~cm}^2
  3. C2 cm22 \mathrm{~cm}^2
  4. D4 cm24 \mathrm{~cm}^2

Correct answer

D. 4 cm24 \mathrm{~cm}^2

Step-by-step solution

Given, square wire of side =2 cm=2 \mathrm{~cm}, u=−20 cm,f=−10 cmu=-20 \mathrm{~cm}, f=-10 \mathrm{~cm}, Area of second wire = ? ∴1v+1u=1f⇒1v+1(−20)=1−10⇒1v=−110+120⇒v=−20 cm\begin{aligned} & \therefore & \frac{1}{v}+\frac{1}{u} & =\frac{1}{f} \\ & \Rightarrow & \frac{1}{v}+\frac{1}{(-20)} & =\frac{1}{-10} \Rightarrow \frac{1}{v}=-\frac{1}{10}+\frac{1}{20} \\ & \Rightarrow & v & =-20 \mathrm{~cm}\end{aligned} We know that, m=-\frac{v}{u}=\frac{-(-20)}{-20}=-1 \because \quad \frac{\text{ Area of image }}{\text{ Area of object }}=m^2 \Rightarrow \frac{A_i}{A_0}=(-1)^2 \frac{A_i}{2 \times 2}=1\Rightarrow \quad A_i=4 \mathrm{~cm}^2
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