A beam of diameter `d` is incident on a glass hemiphere as shown.If the radius of curvature of the hemiphere is very large in composition to d, then the diameter of the beam at the base of the hemiphere will be :

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Solution

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:

$n 2 / v - n 1 / u = (n 2 - n 1) / R$

$(3 / 2) / V = (1 / 2) / R$

$v = 3 R$

for similar triangles ABC and ADE

$D 1 / 2 r = D / 3 R$

$D 1 = (2 / 3) D$

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A beam of diameter `d` is incident on a glass hemiphere as shown.If the radius of curvature of the hemiphere is very large in composition to d, then the diameter of the beam at the base of the hemiphere will be :

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