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.
$\therefore (B,C,D)$