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Answer 1

Question :

The diagram show a semi-circilar glass block.

Which diagram correctly shows the path of the ray of light and the critical angle C?

Answer : Diagram (A)

Solution :

❒ Critical angle is the angle made in denser medium for which the angle of refraction in rarer medium is 90°.

• When angle in denser medium is more then critical angle the light ray reflects back in denser medium following the law of reflection and the interface behaves like a perfectly reflecting mirror.

See the attachment for better understanding!

• O = Object
• NN' = Normal to the interface
• II' = Interface
• C = Critical angle
• AB = reflected ray due to TIR

When i = C then r = 90°

$\sf:\implies\:n_d\:sin(i)=n_r\:sin(r)$

$\sf:\implies\:n_d\:sinC=n_r\:sin90^{\circ}$

$\sf:\implies\:sinC=\dfrac{n_r}{n_d}$

$:\implies\:\underline{\boxed{\bf{\gray{C=sin^{-1}\dfrac{n_r}{n_d}}}}}$

Knowledge BoosteR :

Conditions of TIR :

• Light is incident on the interface from denser medium.
• Angle of incidence should be greater than the critical angle (i > C)