A concave mirror of focal length 20 cm forms an virtual image having twice the linear dimension

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A concave mirror of focal length 20 cm forms an virtual...

A concave mirror of focal length $20 \mathrm{~cm}$ forms an virtual image having twice the linear dimensions of the object, the position of the object will be $\mathrm{cm}$
(A) $7.5$
(B) $-10$
(C) 10
(D) $-7.5$

Key Concepts

Magnification

Magnification (m) in mirror systems is defined as the ratio of the image height to the object height and is related to distances by the formula m = -v/u. This concept not only indicates the size change between the object and the image but also provides information on the orientation of the image (inverted or upright).

Mirror Equation

The mirror equation, given by 1/f = 1/u + 1/v, is fundamental in geometrical optics for relating the focal length (f), object distance (u), and image distance (v) of a mirror. It allows one to compute any one quantity if the other two are known and is essential in solving problems related to image formation.

Virtual Image Formation

A virtual image in the context of mirror optics is formed when the reflected rays diverge, and the image appears to be located behind the mirror. In concave mirrors, when the object is placed inside the focal length, the image is formed virtually, is upright, and can be magnified compared to the object.

Sign Conventions in Mirror Optics

Sign conventions are crucial in mirror optics to correctly determine the nature and position of the image. Typically, in the Cartesian sign convention for mirrors, the object distance (u) is positive, the focal length (f) is positive for concave mirrors, and the image distance (v) is negative if the image is virtual. These conventions ensure the correct application of the mirror equation and magnification formula.

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