Question

A monochromatic beam of light is incident at the interface of two materials of refracive index $n _{1}$ and $n _{2}$ as shown. If $n _{1}> n _{2}$ and $\theta_{ c }$ is the critical angle then which of the following statements is NOT true?

• A. $\theta_{1}=\theta_{3}$ for all values of $\theta_{1}$.
• B. $\cos \theta_{2}$ is imaginary for $\theta_{1}>\theta_{c}$.
• C. $\cos \theta_{2}=0$ for $\theta_{1}=\theta_{ c }$.
• D. $\cos \theta_{3}$ is imaginary for $\theta_{1}=\theta_{c}$.

Answer 1

Answer: (D)

$n _{1}> n _{2}$
this means light is going from rarer to denser medium.
So $\theta_{2}$ will always be less than $\theta_{1}$
$n _{2} \sin \theta_{1}= n _{1} \sin \theta_{2}$
So $\cos \left(\theta_{2}\right)$ will never be imaginary and also $\theta_{2}$ can't be $90^{\circ}$
In question incorrect options are asked.
$\therefore ( B , C , D )$