# 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.

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}