Question

A ray of light passes through an equilateral glass prism, such that the angle of incidence is equal to the angle of emergence. If the angle of emergence is $\frac{3}{4}$times the angle of prism. The refractive index of the glass prism is:

• A. 1.5
• B. 1.414
• C. 1.616
• D. 1.7

Answer 1

The correct option is B 1.414

$i=e$
$\therefore r_1=r_2$
$r_1+r_2+180-A=180$
$A=r_1+r_2$
$r_2=r_1=A/2$

$\frac{sini}{sin{r}_1}=\mu$

$\mu =\frac{sin\left(3A/4\right)}{sin\left(A/2\right)}$

$=\frac{sin\left(\frac{3\times 60}{4}\right)}{sin\left(60/2\right)}$

$=\frac{sin45}{sin30}$

$=\sqrt{2}$

$=1.414$