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Question

One end of a cylindrical rod is grounded to a hemispherical surface of radius R=20 mm. It is immersed in water of refractive index 1.33. If the refractive index of the hemisphere is 1.5. Find the position of an image of an object placed on the axis of the rod inside water at 10 cm from the pole.

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Solution

Given: One end of a cylindrical rod is grounded to a hemispherical surface of radius R=20mm. It is immersed in water of refractive index 1.33. If the refractive index of the hemisphere is 1.5.
To find the position of an image of an object placed on the axis of the rod inside water at 10 cm from the pole.
Solution:
As per the given condition,
Refractive index of water, μ1=1.33
Refractive index of the hemisphere, μ2=1.5
Radius of curvature, R=20mm=2cm
object distance, u=10cm
Substituting these values in the following formula, we get
μ2vμ1u=μ2μ1R1.5v1.3310=1.51.3321.5v=0.1721.33101.5v=(0.17×5)1.3310v=1.5×10(0.48)v=31.25cm
is the required position of an image of an object placed on the axis of the rod.

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