# A beam of light passes from quartz to zircon at an angle of 19°. What is the angle of refraction? What is the critical angle when passing from zircon to quartz?

Jun 3, 2016

$r = {14.88}^{o}$

${\theta}_{C} = 51.98 {\text{ }}^{o}$

#### Explanation:

$\text{assuming "n_q=1.544 " , " " n_z=1.960 " ,} \sin 19 = 0.326$

$\text{using Snell law:}$

${n}_{q} \cdot \sin i = {n}_{z} \cdot \sin r$

$1.544 \cdot \sin 19 = 1.960 \cdot \sin r$

$1.544 \cdot 0.326 = 1.960 \cdot \sin r$

$0.503344 = 1.960 \cdot \sin r$

$\sin r = \frac{0.503344}{1.960}$

$r = {14.88}^{o}$

$\text{critical angle for light passing from zircon to quartz:}$

${\theta}_{C} = \text{ critical angle}$

$\sin {\theta}_{C} \cdot {n}_{z} = \sin 90 \cdot {n}_{q}$

so; sin 90=1

$\sin {\theta}_{C} \cdot {n}_{z} = 1 \cdot {n}_{q}$

$\sin {\theta}_{C} = {n}_{q} / {n}_{z} = \frac{1.544}{1.960}$

${\theta}_{C} = 51.98 {\text{ }}^{o}$