#### Question

A dentist's mirror has a radius of curvature of 3 cm. How far must it be placed from a small dental cavity to give a virtual image of the cavity that is magnified five times?

#### Solution

Given,

The dentist's mirror is a concave mirror.

Radius of curvature 'R' = -3 cm

Therefore, the

focal length of the mirror `f=R/2=(-3)/2=-1.5 `cm

Given that magnification 'm' = 5

Therefore, using the magnification formula, we get `m=-v/u`

`v=-mu`

`V=-5u`

Now, using the mirror formula, we get

`1/f=1/v+1/u`

`1/(-1.5)=1/-5u+1/u`

⇒ `1/-1.5=1/(-5u)+1/u`

⇒ `-1/1.5=1/(-5u)+5/(5u)=4/(5u)`

⇒ `u=((-1.5)xx4)/5=(-6)/5`

⇒ `u=-1.2 cm`

The dentist should place the object at a distanc of 1.2 cm from the mirror.

focal length of the mirror` f=R_2=32=1.5 cm`

Is there an error in this question or solution?

Solution A Dentist'S Mirror Has a Radius of Curvature of 3 Cm. How Far Must It Be Placed from a Small Dental Cavity to Give a Virtual Image of the Cavity that is Magnified Five Times? Concept: Mirror Formula and Magnification.