Question

A ray of light incident at an angle $\theta$ on a refracting face of a prism emerges from the other face normally. If the angle of the prism is $5^{\circ}$ and the prism is made of a material of refractive index $1.5$, the angle of incidence is

• A. $7.5^{\circ}$
• B. $5^{\circ}$
• C. $15^{\circ}$
• D. $2.5^{\circ}$

Answer 1

Answer: (A)

According to the question, ray emerges from other surface of prism normally,
$\therefore $ Angle of incidence at second face,

$r' = 0^{\circ}$
Now, $r+r' = A$
$\Rightarrow r = A -r' = 5^{\circ} - 0^{\circ} = 5^{\circ}$
Using snell's law
$\mu = \frac{sin\,i}{sin\,r}$
or $sin\,i = \mu sin\,r = 1.5 \times sin 5^{\circ} $
$ = 0.131$
$\Rightarrow \theta = i = sin ^{-1} (0.131) $
$ = 7.5^{\circ}$