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

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

Vedclass · Accepted Answer

$180^\circ - 2A$

Vedclass · Answer

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

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

Similar Questions

If $\frac{\sin^2 x + 1}{2\sin^2 x - 5\sin x + 3} = \frac{A}{2\sin x - 3} + \frac{B}{\sin x - 1} + C$,then:

In a Ruby laser, the colour of laser light is due to ______ atom.

Which of the following reagents is used to distinguish acetone and acetophenone?

Two identical capacitors $A$ and $B$ are charged to the same potential $V$ and are connected in two circuits at $t = 0$,as shown in the figure. The charge on the capacitors at time $t = CR$ are respectively:

$A$ frictionless track $ABCDE$ ends in a circular loop of radius $R$. $A$ body slides down the track from point $A$ which is at a height $h = 5 \, cm$. The maximum value of $R$ for the body to successfully complete the loop is .................. $cm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module