The angle of a prism made of a material of re | vedclass

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

Question

(B) Let the prism angle be $A = 90^{\circ}$ and refractive index be $\mu = \sqrt{2}$.For total internal reflection $(TIR)$ at the second face, the ang

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(B) Let the prism angle be $A = 90^{\circ}$ and refractive index be $\mu = \sqrt{2}$.For total internal reflection $(TIR)$ at the second face, the angle of incidence at the second face $r_2$ must be greater than or equal to the critical angle $C$.The critical angle $C$ is given by $\sin C = \frac{1}{\mu} = \frac{1}{\sqrt{2}}$, which gives $C = 45^{\circ}$.Thus, for $TIR$, $r_2 > 45^{\circ}$.From the geometry of the prism, $r_1 + r_2 = A = 90^{\circ}$.Substituting $r_2 > 45^{\circ}$, we get $r_1 Using Snell's law at the first face: $\sin i = \mu \sin r_1$.Since $r_1 Therefore, $\sin i However, for the light to enter the prism and satisfy the condition, we look for the boundary condition where $r_2 = 45^{\circ}$, which implies $r_1 = 45^{\circ}$.Then $\sin i = \sqrt{2} \sin 45^{\circ} = \sqrt{2} 	imes \frac{1}{\sqrt{2}} = 1$, so $i = 90^{\circ}$.Since the question asks for the condition for $TIR$, any angle of incidence $i  45^{\circ}$ which leads to $r_2 < 45^{\circ}$ (no $TIR$). Thus, the boundary is at $i = 90^{\circ}$.

The angle of a prism made of a material of refractive index $\sqrt{2}$ is $90^{\circ}$. The angle of incidence for a light ray on the first face of the prism such that the light ray suffers total internal reflection at the second face is (in $^{\circ}$)

Similar Questions

$A$ light ray is incident on a prism of angle $A = 30^{\circ}$ at an angle of incidence of $60^{\circ}$. If the emergent ray makes an angle of $30^{\circ}$ with the incident ray,then find the refractive index of the prism $:-$

The angle of a prism is $A$. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence $2A$ on the first surface return back through the same path after suffering reflection at the silvered surface. The refractive index $\mu$ of the prism is:

$A$ prism has a refractive index $\sqrt{3/2}$ and a refracting angle of $90^o$. Find the minimum deviation produced by the prism in degrees.

$A$ yellow light undergoes minimum deviation through a prism. If $i_1$ and $i_2$ are the angle of incidence and the angle of emergence respectively,then:

At what angle of incidence should a ray of light be incident on a face of an equilateral prism if the angle of minimum deviation is $46^{\circ}$ (in $^{\circ}$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module