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.
