A ray of light incident on one face of an equ | vedclass

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

Question

(A) For an equilateral prism, the angle of the prism $A = 60^{\circ}$.Given refractive index $\mu = \sqrt{2}$.The emergent ray grazes the adjacent fac

Vedclass · Accepted Answer

$\sin^{-1} (\sqrt{2} \sin 15^{\circ})$

Vedclass · Answer

(A) For an equilateral prism, the angle of the prism $A = 60^{\circ}$.Given refractive index $\mu = \sqrt{2}$.The emergent ray grazes the adjacent face, which means the angle of emergence $e = 90^{\circ}$.At the second face, by Snell's law: $\mu \sin r_2 = 1 \cdot \sin e$.$\sqrt{2} \sin r_2 = \sin 90^{\circ} = 1 \implies \sin r_2 = 1/\sqrt{2} \implies r_2 = 45^{\circ}$.Since $r_1 + r_2 = A$, we have $r_1 + 45^{\circ} = 60^{\circ} \implies r_1 = 15^{\circ}$.Applying Snell's law at the first face: $1 \cdot \sin i = \mu \sin r_1$.$\sin i = \sqrt{2} \sin 15^{\circ} \implies i = \sin^{-1} (\sqrt{2} \sin 15^{\circ})$.

$A$ ray of light incident on one face of an equilateral glass prism having refractive index $\sqrt{2}$, produces the emergent ray which just grazes along the adjacent face. The value of angle of incidence is $(\sin 90^{\circ} = 1, \sin 30^{\circ} = 0.5, \sin 45^{\circ} = 1/\sqrt{2})$.

Similar Questions

When a ray of light is incident normally on one refracting surface of an equilateral prism (Refractive index of the material of the prism $= 1.5$),what happens to the ray at the second refracting surface?

If a prism having refractive index $\sqrt{3}$ has an angle of minimum deviation equal to the refracting angle of the prism,then the refracting angle of the prism is......$^o$

Which of the following prisms is used to see the infrared spectrum of light?

The refracting angle of a prism is $60^{\circ}$ and the refractive index is $\sqrt{7/3}$ relative to the surroundings. The limiting angle of incidence of a ray that will be transmitted through the prism is ......$^{\circ}$

The minimum deviation produced by a hollow prism filled with a certain liquid is found to be $30^{\circ}$. The light ray is also found to be refracted at an angle of $30^{\circ}$. Then the refractive index of the liquid is

Vedclass Test Series

Exam Paper Generator

Online Exam Module