Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
9th Edition
ISBN: 9781305932302
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 35, Problem 31P
To determine

The expected angle of refraction in the sheet 3.

Expert Solution & Answer
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Answer to Problem 31P

The expected angle of refraction in the sheet 3 is 23.1°.

Explanation of Solution

Assume n1, n2 and n3 as the refractive indices of sheets 1, 2 and 3 respectively.

The following figure shows the refraction of the laser beam when the sheet 1 is placed on top of the sheet 2.

Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term, Chapter 35, Problem 31P , additional homework tip  1

Figure-(1)

Write the equation using Snell’s law in the above figure.

    sinisin(26.5°)=n1                                                                                                         (I)

Here, i is the angle of incidence on the sheet 1.

Write the equation using Snell’s law in the figure-(1).

    sin(26.5°)sin(31.7°)=n2n1                                                                                                      (II)

The following figure shows the refraction of the laser beam when the sheet 3 is placed on top of the sheet 2.

Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term, Chapter 35, Problem 31P , additional homework tip  2

Figure-(2)

Write the equation using Snell’s law in the above figure.

    sinisin(r)=n3sinr=sinin3                                                                                                          (III)

Here, r is the angle of refraction in the sheet 3.

Write the equation using Snell’s law in the figure-(2).

    sin(r)sin(36.7°)=n2n3sin(r)=n2n3sin(36.7°)                                                                                     (IV)

Compare the equations (III) and (IV).

    sinin3=n2n3sin(36.7°)n2=sinisin(36.7°)                                                                                                (V)

The following figure shows the refraction of the laser beam when the sheet 1 is placed on top of the sheet 3.

Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term, Chapter 35, Problem 31P , additional homework tip  3

Figure-(3)

Write the equation using Snell’s law in the above figure.

    sinisin(r)=n1sin(r)=n1(sini)                                                                                                   (VI)

Here, r is the angle of refraction in the sheet 1.

Write the equation using Snell’s law in the figure-(2).

    sin(r)=n3n1sin(θ)                                                                                                (VII)

Here, θ is the angle of refraction in the sheet 3.

Compare the equations (VI) and (VII).

    n1(sini)=n3n1sin(θ)sinisinθ=n3                                                                                            (VIII)

The angle of refraction in the sheet 1 when the sheet 1 is placed on top of the sheet 3 is equal to the angle of refraction in the sheet 1 when the sheet 1 is placed on top of the sheet 2.

    r=26.5°

The angle of refraction in the sheet 3 when the sheet 3 is placed on top of the sheet 2 is equal to the angle of refraction in the sheet 1 when the sheet 1 is placed on top of the sheet 2.

    r=26.5°

Rewrite the equation (IV).

    sin(26.5°)sin(36.7°)=n2n3n3n2=sin(36.7°)sin(26.5°)

Rewrite the equation (II).

    n2n1=sin(26.5°)sin(31.7°)

Conclusion:

Substitute 26.5° for r in the equation (VII).

    sin(26.5°)=n3n1sin(θ)sin(26.5°)sin(θ)=n3n1sin(26.5°)sin(θ)=n3n2×n2n1

Substitute sin(36.7°)sin(26.5°) for n3n2 and sin(26.5°)sin(31.7°) for n2n1 in the above equation to calculate the angle of refraction in the sheet 3.

    sin(26.5°)sin(θ)=sin(36.7°)sin(26.5°)×sin(26.5°)sin(31.7°)sinθ=0.3923θ=23.1°

Therefore, the expected angle of refraction in the sheet 3 is 23.1°.

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Chapter 35 Solutions

Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term

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Laws of Refraction of Light | Don't Memorise; Author: Don't Memorise;https://www.youtube.com/watch?v=4l2thi5_84o;License: Standard YouTube License, CC-BY