A ray of light is incident on the hypotenuse | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) For total internal reflection to occur at the hypotenuse,the angle of incidence $i$ must be greater than or equal to the critical angle $C$.Here,t

Vedclass · Accepted Answer

$\cos ^{-1}\left(\frac{1}{\mu}\right)$

Vedclass · Answer

(D) For total internal reflection to occur at the hypotenuse,the angle of incidence $i$ must be greater than or equal to the critical angle $C$.Here,the ray travels parallel to the base. From the geometry of the right-angled prism,the angle of incidence $i$ at the hypotenuse is $(90^{\circ} - 	heta)$,where $	heta$ is the base angle.For total internal reflection,$i \geq C$,where $\sin C = \frac{1}{\mu}$.Thus,the condition is $i \geq \sin^{-1}\left(\frac{1}{\mu}ight)$.Substituting $i = 90^{\circ} - 	heta$,we get $90^{\circ} - 	heta \geq \sin^{-1}\left(\frac{1}{\mu}ight)$.Taking the sine of both sides: $\sin(90^{\circ} - 	heta) \geq \frac{1}{\mu}$.This simplifies to $\cos 	heta \geq \frac{1}{\mu}$.Therefore,the maximum value of the base angle $	heta$ is $\cos^{-1}\left(\frac{1}{\mu}ight)$.

$A$ 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

Similar Questions

Which of the following hydrides has the lowest boiling point?

The inverse of the proposition $(p \wedge \sim q) \Rightarrow r$ is

If a copper rod carries a direct current,the magnetic field associated with the current will be

What is the coordination number of the metal in $[Co(en)_2Cl_2]^+$?

Let $R_1$ be a relation defined by $R_1 = \{(a, b) | a \geq b, a, b \in \mathbb{R}\}$. Then $R_1$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module