Question

A dentist mirror has a radius of curvature of 3 cm. How far must it will be placed from a small dental cavity to give a virtual image of the cavity that is magnified 5 times

Answer 1

As per the question the image should definitely be highly enlarged that is m=+5 the object should be kept at focus R=2f then,f=R/2 i.e.3/2 =1.5

Answer 2

Answer:

Mirror should be placed at the distance of 1.2cm.

Explanation:

Given,

A dentist mirror has a radius of curvature of 3 cm.

To find: How far must it will be placed from a small dental cavity to give a virtual image of the cavity that is magnified 5 times.

Solution:

Using Sign convention,

Radius of curvature = r = -3 [because of concave mirror]

Then, Focal Length = f = r/2 = 3/2 = -1.5

It is magnified(m) by 5 times.

i.e -v/u = 5

or, v = -5u

Using Mirror Formula,

1/v+1/u = 1/f

Substituting the values,

or, 1/(-5u) + 1/u = 1/(-1.5)

or, u=-1.2 cm

Therefore, Mirror should be placed at the distance of 1.2cm.