AP EAMCET · PHYSICS · Ray Optics
A ray of light is incident on the hypotenuse of a right-angled prism after travelling parallel to the base inside the prism. If \(\mu\) is the refractive index of the material of the prism, the maximum value of the base angle for which light is totally reflected from the hypotenuse is
- A \(\sin ^{-1}\left(\frac{1}{\mu}\right)\)
- B \(\tan ^{-1}\left(\frac{1}{\mu}\right)\)
- C \(\sin ^{-1}\left(\frac{\mu-1}{\mu}\right)\)
- D \(\cos ^{-1}\left(\frac{1}{\mu}\right)\)
Answer & Solution
Correct Answer
(D) \(\cos ^{-1}\left(\frac{1}{\mu}\right)\)
Step-by-step Solution
Detailed explanation
For total internal reflection, \(\mu=\frac{1}{\sin C}\) \(\mu=\frac{1}{\sin \left(90^{\circ}-\theta\right)}\) \(\mu=\frac{1}{\cos \theta} \Rightarrow \cos \theta=\frac{1}{\mu}\) \(\theta=\cos ^{-1}\left(\frac{1}{\mu}\right)\)
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