A ray of light strikes a transparent slab of the refractive index of $\sqrt{2}$ at an angle of incidence $45°$. The angle between the reflected and refracted rays is

• A

  $95°$
• B

  $120°$
• C

  $135°$
• Correct answer
  D

  $105°$

Solution

According to the figure,

Given, $i=45°$

Let the angle between the reflected ray and refracted ray is



Apply Snell's law at the air-glass surface,

$\frac{\sin i}{\sin r}=\frac{n}{1}$

$\Rightarrow \frac{\sin 45°}{\sin r}=\sqrt{2}$

$\sin r=\frac{1}{\sqrt{2}\cdot \sqrt{2}}=\frac{1}{2}$

$\therefore r=30°$

From the diagram, $\theta =180-\left(i+r\right)$

$=180-\left(45°+30°\right)$

$=180°-75°=105°$

Hence, the correct answer is option: 'D'.