(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.
<h3>What is Critical angles?</h3>
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
where;
is the refractive index of air = 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:


Critical angles for polystyrene


Critical angles for Sodium Chloride


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"