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

## Question:

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

## Image Formation by Concave Mirror:

A concave mirror forms real, inverted and magnified image, when the real object is positioned between the focal point and the center of curvature of the mirror.

Given Data

• magnification by concave mirror, m = -2 ( negative indicates inverted image)
• object distance, u = 22 cm

Finding the image distance (v)

The magnification can be expressed as:

• {eq}m\ = \dfrac{-v}{u} {/eq}
• {eq}-2\ = \dfrac{-v}{u} {/eq}
• {eq}v\ = 2\times u{/eq}
• {eq}v\ = 2\times 22\ = 44\ cm{/eq}

Finding the focal length (f) of the mirror

Applying the mirror equation:

• {eq}\dfrac{1}{v}\ + \dfrac{1}{u}\ = \dfrac{1}{f} {/eq}
• {eq}\dfrac{1}{44}\ + \dfrac{1}{22}\ = \dfrac{1}{f} {/eq}
• {eq}f\ = 14.7\ cm{/eq} 