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?

Answer 1

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`