The refracting angle of a prism is A, and the | vedclass

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

Question

(B) The formula for the refractive index $\mu$ of a prism in terms of the refracting angle $A$ and the angle of minimum deviation $\delta$ is given by

Vedclass · Accepted Answer

$180^o-2A$

Vedclass · Answer

(B) The formula for the refractive index $\mu$ of a prism in terms of the refracting angle $A$ and the angle of minimum deviation $\delta$ is given by:$\mu = \frac{\sin((A+\delta)/2)}{\sin(A/2)}$Given $\mu = \cot(A/2) = \frac{\cos(A/2)}{\sin(A/2)},$ we substitute this into the formula:$\frac{\cos(A/2)}{\sin(A/2)} = \frac{\sin((A+\delta)/2)}{\sin(A/2)}$Canceling $\sin(A/2)$ from both sides,we get:$\cos(A/2) = \sin((A+\delta)/2)$Using the trigonometric identity $\cos(	heta) = \sin(90^o - 	heta)$:$\sin(90^o - A/2) = \sin((A+\delta)/2)$Equating the angles:$90^o - A/2 = (A+\delta)/2$$180^o - A = A + \delta$$\delta = 180^o - 2A$

The refracting angle of a prism is $A,$ and the refractive index of the material of the prism is $\cot(A/2).$ The angle of minimum deviation is:

Similar Questions

In the given figure,what is the angle of the prism?

For a thin symmetric prism made of glass (refractive index $1.5$),the ratio of the angle of incidence to the angle of minimum deviation is . . . . . . .

What is the maximum value of the refractive index of the material of a prism with prism angle $A$ such that light can pass through it?

When a white light passes through a hollow prism,then

$A$ prism of refractive index $\sqrt{2}$ has a refracting angle of $60^{\circ}$. In order for a ray to suffer minimum deviation,it should be incident at an angle of .......$^{\circ}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module