A ray of light passes from vacuum into a medi | vedclass

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

Question

(B) According to Snell's law,$n_1 \sin i = n_2 \sin r$.Here,$n_1 = 1$ (vacuum),$n_2 = n$,$i$ is the angle of incidence,and $r$ is the angle of refract

Vedclass · Accepted Answer

$2 \operatorname{Cos}^{-1}\left(\frac{n}{2}\right)$

Vedclass · Answer

(B) According to Snell's law,$n_1 \sin i = n_2 \sin r$.Here,$n_1 = 1$ (vacuum),$n_2 = n$,$i$ is the angle of incidence,and $r$ is the angle of refraction.Given that $i = 2r$,we have $r = \frac{i}{2}$.Substituting these into Snell's law:$1 	imes \sin i = n \sin \left(\frac{i}{2}ight)$Using the trigonometric identity $\sin i = 2 \sin \left(\frac{i}{2}ight) \cos \left(\frac{i}{2}ight)$:$2 \sin \left(\frac{i}{2}ight) \cos \left(\frac{i}{2}ight) = n \sin \left(\frac{i}{2}ight)$Dividing both sides by $\sin \left(\frac{i}{2}ight)$ (assuming $i 
eq 0$):$2 \cos \left(\frac{i}{2}ight) = n$$\cos \left(\frac{i}{2}ight) = \frac{n}{2}$$\frac{i}{2} = \cos^{-1} \left(\frac{n}{2}ight)$$i = 2 \cos^{-1} \left(\frac{n}{2}ight)$

$A$ ray of light passes from vacuum into a medium of refractive index $n$. If the angle of incidence is twice the angle of refraction,then the angle of incidence in terms of refractive index is

Similar Questions

$A$ light ray is incident on a transparent sphere of refractive index $\mu = \sqrt{2}$ at an angle of incidence $i = 45^{\circ}$. What is the total deviation of a ray that enters the sphere,undergoes two internal reflections,and then refracts out into the air (in $^{\circ}$)?

$A$ medium shows the relation between $\sin i$ and $\sin r$ as shown in the graph. If the speed of light in the medium is $nc$,then the value of $n$ is:

When light travels from glass to air,the incident angle is ${\theta _1}$ and the refracted angle is ${\theta _2}$. The true relation is:

If ${ }_{i} \mu_{j}$ represents the refractive index when a ray goes from medium $i$ to medium $j$,then the product ${ }_2 \mu_1 \times { }_3 \mu_2 \times { }_4 \mu_3$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module