A beam of diameter ëdí is incident on a glass hemisphere as shown. If the radius of curvature of the hemisphere is very large in comparison to d, then the diameter of the beam at the base of the hemisphere will be
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Given :
D is the diameter of incident light on glass hemisphere.
Let D1 be the diameter of the beam at the base of hemisphere
For objects at infinity Image will be formed at :
Applying the formula for the spherical curved surfaces:
n2/v-n1/u=(n2-n1)/R
(3/2)/V=(1/2)/R
v=3R
for similar triangles ABC and ADE
D1/2r=D/3R
D1=(2/3)D
D is the diameter of incident light on glass hemisphere.
Let D1 be the diameter of the beam at the base of hemisphere
For objects at infinity Image will be formed at :
Applying the formula for the spherical curved surfaces:
n2/v-n1/u=(n2-n1)/R
(3/2)/V=(1/2)/R
v=3R
for similar triangles ABC and ADE
D1/2r=D/3R
D1=(2/3)D
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