A concave mirror has a focal length of 37 cm. Determine the object position for which the...

Question:

A concave mirror has a focal length of 37 cm. Determine the object position for which the resulting image is upright and four times the size of the object. Answer in units of cm.

Concave Mirror:

A concave mirror can form upright and magnified image of the object. Such image forms behind the concave mirror and are virtual. To form virtual image by a concave mirror, object must be positioned between focal point and the pole of the mirror.

Answer and Explanation:

Given Data

  • focal length of concave mirror, {eq}f\ = 37\ cm{/eq}
  • magnification, {eq}m\ = 4{/eq}

Finding the position of the object (u)

Let the image position be v.

The magnification can be expressed as:

  • {eq}m\ = \dfrac{-v}{u} {/eq}
  • {eq}4\ = \dfrac{-v}{u} {/eq}
  • {eq}v\ = -4\times u {/eq}

Applying the mirror equation:

  • {eq}\dfrac{1}{v}\ + \dfrac{1}{u}\ = \dfrac{1}{f} {/eq}
  • {eq}\dfrac{1}{-4\times u}\ + \dfrac{1}{u}\ = \dfrac{1}{37} {/eq}
  • {eq}u\ = 27.75\ 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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