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Question: The index of refraction of benzene is1.8. What is the critical angle for a light ray traveling in benzene toward a flat layer of air above the benzene?

Short Answer

Expert verified

The critical angle for the light ray is θb=33.7∘≈34∘.

Step by step solution

01

Given

The refractive index is nb=1.8.

02

Determine the concept for the Snell’s law as:

Write for the angle of refraction in terms of the vertex angle from the geometry of the prism and the ray diagram. Then using the formula for the exterior angle of triangle, solve for the angle of incidence in terms of the vertex angle. Then, using Snell’s law of refraction, show that the index of refraction of the glass prism is:

n=sin12(ψ+f)sin12f

Formula:

n1²õ¾±²Ôθ1=n2²õ¾±²Ôθ2

03

Calculate the critical angle for a light ray traveling in benzene toward a flat layer of air above the benzene

Snell’s law of refraction gives that

n1²õ¾±²Ôθ1=n2²õ¾±²Ôθ2nb²õ¾±²Ôθa=na²õ¾±²Ôθa²õ¾±²Ôθb=nanb²õ¾±²Ôθa²õ¾±²Ôθb=11.8sin90∘

Substitute the values and solve as:

²õ¾±²Ôθb=0.55θb=33.7∘≈34∘

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