If a prism having refractive index sqrt{3} ha | vedclass

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

Question

(C) Given that the angle of minimum deviation $\delta_{m}$ is equal to the refracting angle of the prism $A$,so $\delta_{m} = A$.The formula for the r

Vedclass · Accepted Answer

$60$

Vedclass · Answer

(C) Given that the angle of minimum deviation $\delta_{m}$ is equal to the refracting angle of the prism $A$,so $\delta_{m} = A$.The formula for the refractive index $\mu$ of a prism is given by $\mu = \frac{\sin((A + \delta_{m})/2)}{\sin(A/2)}$.Substituting $\delta_{m} = A$ into the formula:$\mu = \frac{\sin((A + A)/2)}{\sin(A/2)} = \frac{\sin(A)}{\sin(A/2)}$.Using the trigonometric identity $\sin(A) = 2 \sin(A/2) \cos(A/2)$:$\mu = \frac{2 \sin(A/2) \cos(A/2)}{\sin(A/2)} = 2 \cos(A/2)$.Given $\mu = \sqrt{3}$,we have:$\sqrt{3} = 2 \cos(A/2)$$\cos(A/2) = \frac{\sqrt{3}}{2}$.Since $\cos(30^{\circ}) = \frac{\sqrt{3}}{2}$,we get:$A/2 = 30^{\circ}$$A = 60^{\circ}$.

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......$^o$

Similar Questions

In a thin prism of glass (refractive index $\mu = 1.5$),which of the following relations between the angle of minimum deviation $\delta_m$ and the angle of refraction $r$ is correct?

$A$ prism $(\mu = 1.5)$ has a refracting angle of $30^\circ$. The deviation of a monochromatic ray incident normally on one of its surfaces will be $(\sin 48^\circ 36' = 0.75)$.

If one face of a prism of prism angle $30^{\circ}$ and refractive index $\mu = \sqrt{2}$ is silvered,the incident ray retraces its initial path. The angle of incidence is.......$^{\circ}$

If the angle of minimum deviation is equal to the angle of an equilateral prism,then the speed of light inside the prism is .....

$A$ certain prism is found to produce a minimum deviation of $38^\circ$. It produces a deviation of $44^\circ$ when the angle of incidence is either $42^\circ$ or $62^\circ$. What is the angle of incidence when it is undergoing minimum deviation (in $^\circ$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module