# A dentist uses a small mirror with a radius of 40 mm to locate a cavity in a patient's tooth. If...

## Question:

A dentist uses a small mirror with a radius of {eq}40 \ mm {/eq} to locate a cavity in a patient's tooth. If the mirror is concave and is held {eq}16 \ mm {/eq} from the tooth, what is the magnification of the image?

## Concave Mirror: Application:

A concave mirror is used by dentists to view the magnified image of the tooth cavity. For the object position within the focal point of the concave mirror, an upright, virtual and magnified image forms behind the concave mirror.

Given Data

• Radius of curvature of concave mirror, R = 40 mm
• object (tooth) distance, u = 16 mm

Finding the magnification (m) of the image

Focal length of the mirror is f = R/2 = 40/2 = 20 mm

Let v be the image distance.

Applying mirror equation:

• {eq}\dfrac{1}{v}\ +\dfrac{1}{u}\ = \dfrac{1}{f} {/eq}
• {eq}\dfrac{1}{v}\ +\dfrac{1}{16}\ = \dfrac{1}{20} {/eq}
• {eq}v\ = -80\ mm{/eq}

Now, the magnification is calculated as:

• {eq}m\ = \dfrac{-v}{u} {/eq}
• {eq}m\ = \dfrac{-(-80\ mm)}{16\ mm} {/eq}
• {eq}m\ = 5{/eq}