Material A has a critical angle {i_A}, and ma | vedclass

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

Question

(D) We know that the critical angle $C$ is given by $C = {\sin ^{ - 1}}\left( {\frac{1}{\mu }} \right)$.Given that the critical angle ${i_B} > {i_A}$,

Vedclass · Accepted Answer

$(ii)$ and $(iv)$

Vedclass · Answer

(D) We know that the critical angle $C$ is given by $C = {\sin ^{ - 1}}\left( {\frac{1}{\mu }} \right)$.Given that the critical angle ${i_B} > {i_A}$,it implies that the refractive index ${\mu _B} This means material $B$ is optically rarer and material $A$ is optically denser.Total internal reflection occurs when light travels from a denser medium to a rarer medium. Therefore,light can be totally internally reflected when it passes from $A$ to $B$. Thus,statement $(ii)$ is correct.Now,the critical angle ${C_{AB}}$ for the interface between $A$ and $B$ is given by ${C_{AB}} = {\sin ^{ - 1}}\left( {\frac{{{\mu _B}}}{{{\mu _A}}}} \right)$.Since $\sin {i_A} = \frac{1}{{{\mu _A}}}$ and $\sin {i_B} = \frac{1}{{{\mu _B}}}$,we have ${\mu _A} = \frac{1}{{\sin {i_A}}}$ and ${\mu _B} = \frac{1}{{\sin {i_B}}}$.Substituting these values,we get ${C_{AB}} = {\sin ^{ - 1}}\left( {\frac{{1/\sin {i_B}}}{{1/\sin {i_A}}}} \right) = {\sin ^{ - 1}}\left( {\frac{{\sin {i_A}}}{{\sin {i_B}}}} \right)$. Thus,statement $(iv)$ is correct.

Similar Questions

Assertion : In optical fibre,the diameter of the core is kept small.
Reason : This smaller diameter of the core ensures that the fibre should have incident angle more than the critical angle required for total internal reflection.

$A$ ray of light is incident at an angle $i$ from a denser to a rarer medium. The reflected and the refracted rays are mutually perpendicular. The angle of reflection is $r$ and the angle of refraction is $r'$. Then the critical angle $C$ will be:

The refractive index of the medium is:

$A$ ray of light in a liquid of refractive index $1.4$ approaches the boundary surface between the liquid and air at an angle of incidence whose sine is $0.8$. Which of the following statements is correct about the behavior of the light?

$A$ ray of light refracts from medium $1$ into a thin layer of medium $2$, crosses the layer, and is incident at the critical angle on the interface between medium $2$ and $3$ as shown in the figure. If the angle of incidence of the ray is $\theta$, the value of $\theta$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module