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  • Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having radius of curvature 40 cm. The distance between images formed by the mirror is _______.<div c

Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having radius of curvature 40 cm. The distance between images formed by the mirror is _______.

Option: 1

100 cm


Option: 2

60 cm


Option: 3

160 cm


Option: 4

40 cm


Answers (1)

best_answer

Using Mirror formula

\begin{aligned} & \frac{1}{v}+\frac{1}{u}=\frac{1}{f} \\ & \frac{1}{v}=\frac{1}{f}-\frac{1}{f} \\ & v=\frac{4 f}{u-f} \end{aligned}

For object  \mathrm{A}\left(\mathrm{O}_1\right) \mathrm{u}_{\mathrm{i}}=-15 \mathrm{~cm}, \mathrm{f}=-20 \mathrm{~cm}, \mathrm{~V}_1=?

\begin{aligned} & \mathrm{v}_1=\frac{\mathrm{u}_1 \mathrm{f}}{\mathrm{u}_1-\mathrm{f}}=\frac{(-15)(-20)}{(-15)-(20)}=\frac{+300}{5} \\ & \mathrm{v}_1=+60 \mathrm{~cm} \end{aligned}

For object B \mathrm{B}\left(\mathrm{O}_2\right) \mathrm{u}_2=-25 \mathrm{~cm}, \mathrm{f}=-20 \mathrm{~cm} \mathrm{v}_2=?

\begin{aligned} & \mathrm{v}_2=\frac{\mathrm{u}_2 \mathrm{f}}{\mathrm{u}_2-\mathrm{f}}=\frac{(-25)(-20)}{(-25)-(-20)}=\frac{500}{-5} \\ & \mathrm{v}_2=-100 \mathrm{~cm} \end{aligned}

Hence, the distance between images formed by the mirror is

\mathrm{d}=160 \mathrm{~cm}

Posted by

Suraj Bhandari

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