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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.

Answer and Explanation:

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}

Learn more about this topic:

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What is a Concave Mirror? - Definition, Uses & Equation

from Physics 101: Help and Review

Chapter 14 / Lesson 17
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