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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? - CBSE Class 10 - Science

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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?

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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.
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