A glass hemisphere of radius $0.1 c m$ and refractive index $1.5$ is placed over a spot on a table and the spot is viewed from above. The spot appears to be:

0.1 c m

above the top surface of the hemisphere

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0.1 c m

below the top surface of the hemisphere

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0.033 m

above the top surface of the hemisphere

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exactly on the top surface of the hemisphere

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Solution

The correct option is A $0.1 c m$ above the top surface of the hemisphere
$\frac{n_{0}}{u} + \frac{n_{I}}{v} = \frac{n_{0} - n_{I}}{R}$

$\Rightarrow \frac{1.5}{0.1} + \frac{1}{v} = \frac{0.5}{0.1}$

$\Rightarrow \frac{1}{v} = \frac{0.5}{0.1} - \frac{1.5}{0.1} = \frac{- 1}{0.1}$

$\Rightarrow v = - 0.1 c m$

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A glass hemisphere of radius 0.1 cm and refractive index 1.5 is placed over a spot on a table and the spot is viewed from above. The spot appears to be:

The correct option is A 0.1 cm above the top surface of the hemispheren0u+nIv=n0−nIR⇒1.50.1+1v=0.50.1⇒1v=0.50.1−1.50.1=−10.1⇒v=−0.1cm

A glass hemisphere of radius $0.1 c m$ and refractive index $1.5$ is placed over a spot on a table and the spot is viewed from above. The spot appears to be: