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
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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
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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.
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