# An inverted image is magnified by 2 when the object is placed 22 cm in front of a concave mirror....

## Question:

An inverted image is magnified by 2 when the object is placed 22 cm in front of a concave mirror. Determine the image distance and focal length.

## Relation between {eq}u, v, {/eq} and {eq}f {/eq} for Spherical Mirrors:

As we know the relation between {eq}u, v, {/eq} and {eq}f {/eq} is defined as: {eq}\displaystyle \frac{1}{u} + \frac{1}{v} = \frac{1}{f} {/eq} where:

• {eq}u {/eq} is the object distance from the spherical mirror.
• {eq}v {/eq} is the image distance from the spherical mirror.
• {eq}f {/eq} is the focal length of the spherical mirror.

The lateral magnification is given by: {eq}\displaystyle m = - \frac{v}{u} {/eq}.

Given:

• The lateral magnification is: {eq}m = 2 {/eq}.
• The object distance from the concave mirror is: {eq}u = - 22 \ \rm cm {/eq} (Here the...

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