Question:

A concave mirror of focal length $15 \,cm$ forms an image having twice the linear dimension of the object. The position of the object when die image is virtual will be :

Updated On: Jul 5, 2022
  • 45 cm
  • 30 cm
  • 7.5 cm
  • 22.5 cm
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The Correct Option is C

Solution and Explanation

Focal length of concave mirror $f=-15 \,cm$ magnification $=2$ (for virtual image) Linear magnification $m=\frac{\text { size of image }}{\text { size of object }}=-\frac{v}{u}$ $2=-\frac{v}{u}$ or $v=-2\, u$ Now from the relation $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$ or $-\frac{1}{15}=\frac{1}{u}-\frac{1}{2 u}=\frac{1}{2 u}$ or $2 u=-15$ or $u=-7.5\, cm$
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Concepts Used:

Spherical Mirrors

A spherical mirror is a mirror which has been cut out of a spherical surface. 

There are two kinds of spherical mirrors:

  1. Convex Mirror
  2. Concave Mirror
Spherical Mirrors
Spherical Mirrors

 

 

 

 

 

 

 

 

 

Concave Mirror

Concave mirrors are also called converging mirrors, because in these types of mirrors, light rays converge at a point after impact and reflect back from the reflective surface of the mirror.

Convex Mirror

The convex mirror has a reflective surface that is curved outward. Regardless of the distance between the subject and the mirrors, these mirrors are "always" virtual, upright and reduced.