Question

For light of wavelength 589 nm, calculate the critical angles for the following substances when surrounded by air.

Answer 1

(1) The critical angles for the fused quartz is 44⁰,

(2) The critical angles for the polystyrene is 39⁰.

(3) The critical angles for the sodium chloride is 41⁰.

What is Critical angles?

In optics, the critical angle is the topmost angle at which a shaft of light traveling in one transparent medium can strike the boundary between that medium and another with a lower refractive indicator without being fully reflected within the first

Critical angles for the different medium.

θ$=sin^{-1}\frac{n_{2} }{n_{1} }$

where;

$n_{2}$ is the refractive index of air = 1

$n_{1}$ is the refractive index of the given substances.

Refractive index of quartz glass = 1.46

Refractive index of polystyrene = 1.59

Refractive index of sodium chloride = 1.54

Critical angles for quartz glass:

$\theta_{\text {crit }}=\sin ^{-1} \frac{1.00029}{1.46}$

$\theta_{\text {crit }}=44^{o}$

Critical angles for polystyrene

$\theta_{\text {crit }}=\sin ^{-1} \frac{1.00029}{1.59}$

$\theta_{\text {crit }}=39^{\circ}$

Critical angles for Sodium Chloride

$\theta_{\text {crit }}=\sin ^{-1} \frac{1.00029}{1.54}$

$\theta_{\text {crit }}=41^{o}$

Thus, the critical angles for the quartz glass is 44⁰, the critical angles for the polystyrene is 39 ⁰ and the critical angles for the sodium chloride is 41⁰.

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I understand that the question you are looking for is:

"For light of wavelength 589 nm, calculate the critical angles for the following substances when surrounded by air.

(a) Fused Quartz

(b) Polystyrene

(c) Sodium chloride"