A beam of light passes from zircon to quartz at an incident angle of 8°. What is the angle of refraction?

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A beam of light passes from zircon to quartz at an incident angle of 8°. What is the angle of refraction?

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Answer 1 · 2017-01-04T12:39:47

${9.4}^{\circ}$ $9.4^@$ , rounded to one decimal place.

Explanation:

Refractive index of Zircon and Quartz varies as below

Zircon: $1.81 - 2.024$ $1.81 - 2.024$
Quartz: $1.544 - 1.553$ $1.544 - 1.553$

For this problem the refractive indices of samples are assumed as lowest.

From Snell's law we know that when a beam passes from a medium $1$ $1$ having refractive index $n_{1}$ $n_1$ making and angle $θ_{1}$ $theta_1$ to medium $2$ $2$ having refractive index $n_{2}$ $n_2$ , angle of refraction $θ_{2}$ $theta_2$ is given by the equation

$n_{1} {sin θ}_{1} = n_{2} {sin θ}_{2}$ $n_1 sin theta_1 = n_2 sin theta_2$

Inserting given values we get

$1.81 {sin 8}^{\circ} = 1.544 {sin θ}_{2}$ $1.81 sin 8^@= 1.544 sin theta_2$
$\Rightarrow {sin θ}_{2} = \frac{1.81 {sin 8}^{\circ}}{1.544}$ $=> sin theta_2=(1.81 sin 8^@)/1.544$
$\Rightarrow θ_{2} = {sin}^{- 1} (\frac{1.81 {sin 8}^{\circ}}{1.544})$ $=> theta_2=sin^-1 ((1.81 sin 8^@)/1.544)$
$= {9.4}^{\circ}$ $=9.4^@$ , rounded to one decimal place.

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A beam of light passes from zircon to quartz at an incident angle of 8°. What is the angle of refraction?

1 Answer

Explanation:

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