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To be internally reflected, light must travel from light flint glass

to water … the critical angle is 57.3° …

… according to Snell’s law of refraction … n₁ sin θ₁ = n₂ sin θ₂ …

To be internally reflected … θ₂ = 90° … so that …

… n₁ sin θ₁ = n₂ sin 90° … since the product … n sin θ = constant …

for all media … and since … sin θ … increases as θ increases from 0°

to 90° … n must be minimum if θ = maximum at 90° … since n = 1.33

for water … while n = 1.58 for light flint glass … then n₂ = 1.33 (water)

when θ₂ = maximum at 90° … n₁ = 1.58 ( light flint glass ) …

… according to Snell’s law … n₁ sin θ₁ = n₂ sin 90° = n₂ …

… sin θ₁ = n₂ / n₁ = 1.33 / 1.58 = 0.8418 …

… θ₁ = sin ⁻ ¹ ( 0.8418 ) = 57.3° …