The refractive index of a prism is mu = sqrt{ | vedclass

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

Question

(A) For minimum deviation $\delta_{\min}$,we have $i = e$ and $r_1 = r_2 = \frac{A}{2}$.Given that the ratio of the angle of minimum deviation $\delta

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(A) For minimum deviation $\delta_{\min}$,we have $i = e$ and $r_1 = r_2 = \frac{A}{2}$.Given that the ratio of the angle of minimum deviation $\delta_{\min}$ to the angle of the prism $A$ is $1$,so $\frac{\delta_{\min}}{A} = 1$,which implies $\delta_{\min} = A$.We know that $\delta_{\min} = 2i - A$. Substituting $\delta_{\min} = A$,we get $A = 2i - A$,which simplifies to $2A = 2i$,or $i = A$.Using Snell's law at the first surface: $1 	imes \sin i = \mu \sin r_1$.Substituting $i = A$ and $r_1 = \frac{A}{2}$,we get $\sin A = \mu \sin \left(\frac{A}{2}ight)$.Using the trigonometric identity $\sin A = 2 \sin \frac{A}{2} \cos \frac{A}{2}$,we have $2 \sin \frac{A}{2} \cos \frac{A}{2} = \sqrt{3} \sin \left(\frac{A}{2}ight)$.Dividing both sides by $\sin \left(\frac{A}{2}ight)$ (since $A 
eq 0$),we get $2 \cos \left(\frac{A}{2}ight) = \sqrt{3}$,or $\cos \left(\frac{A}{2}ight) = \frac{\sqrt{3}}{2}$.This implies $\frac{A}{2} = 30^{\circ}$,so $A = 60^{\circ}$.

The refractive index of a prism is $\mu = \sqrt{3}$ and the ratio of the angle of minimum deviation to the angle of the prism is $1$. The value of the angle of the prism is $......^{\circ}$.

Similar Questions

If a thin prism of glass is dipped into water,then the minimum deviation (with respect to air) of light produced by the prism will be: $\left( {_a{\mu _g} = \frac{3}{2} \text{ and } _a{\mu _w} = \frac{4}{3}} \right)$

$A$ ray of light is incident on a $60^{\circ}$ prism at the minimum deviation position. The angle of refraction at the first face (i.e.,incident face) of the prism is.......$^{\circ}$

$A$ prism has a refracting angle of $30^\circ$ and a refractive index of $\mu = \sqrt{2}$. One of its faces is silvered. $A$ ray of light incident on the other face retraces its path. What is the angle of incidence in degrees?

$A$ prism is made up of material of refractive index $\sqrt{3}$. The angle of the prism is $A$. If the angle of minimum deviation is equal to the angle of the prism,then the value of $A$ is: (in $^{\circ}$)

Three prisms $1, 2$ and $3$ have the prism angle $A = 60^o$,but their refractive indices are respectively $1.4, 1.5$ and $1.6$. If $\delta_1, \delta_2, \delta_3$ be their respective angles of deviation,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module