Chapter 33: Q58P (page 1005)

Question: The index of refraction of benzene is $1.8$ . 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 $θ_{b} = 33 . 7^{\circ} \approx 34^{\circ}$ .

Step by step solution

Given

The refractive index is $n_{b} = 1.8$ .

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:

$n = \frac{\sin \frac{1}{2} (ψ + f)}{\sin \frac{1}{2} f}$

Formula:

$n_{1} {sinθ}_{1} = n_{2} {sinθ}_{2}$

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

$n_{1} {sinθ}_{1} = n_{2} {sinθ}_{2} n_{b} {sinθ}_{a} = n_{a} {sinθ}_{a} {sinθ}_{b} = \frac{n_{a}}{n_{b}} {sinθ}_{a} {sinθ}_{b} = \frac{1}{1.8} \sin 90^{\circ}$

Substitute the values and solve as:

$\begin{array}{ll} {sinθ}_{b} = 0.55 \\ θ_{b} = 33 . 7^{\circ} \approx 34^{\circ} \end{array}$

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Question: The index of refraction of benzene is $1.8$ . What is the critical angle for a light ray traveling in benzene toward a flat layer of air above the benzene?

Short Answer

Step by step solution

Given

Determine the concept for the Snell’s law as:

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

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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

Step by step solution

Given

Determine the concept for the Snell’s law as:

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Particle Model of Matter

Torque and Rotational Motion

Mechanics and Materials

Famous Physicists

Electrostatics

Geometrical and Physical Optics

Study anywhere. Anytime. Across all devices.

Question: The index of refraction of benzene is $1.8$ . What is the critical angle for a light ray traveling in benzene toward a flat layer of air above the benzene?