Physics for Scientists and Engineers, Technology Update (No access codes included)
Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 35, Problem 35.40P
To determine

The angular spread of visible light passing through a prism.

Expert Solution & Answer
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Answer to Problem 35.40P

The angular spread of visible light passing through a prism is sin1[nVsin(ϕsin1(sinθnV))]sin1[nRsin(ϕsin1(sinθnR))] .

Explanation of Solution

Given Info:

Explanation:

Write the expression for snell’s law for prism to calculate angle of refraction for red light.

n1sinθ1=n2sin(ϕθ2)sin(ϕθ2)=(n1sinθ1n2)θ2=ϕsin1(n1sinθ1n2) (1)

Here,

n1 is refractive index for air.

θ1 is angle of incidence for red light.

n2 is refractive index for red light.

θ2 is the angle of refraction for red light.

ϕ is the apex angle.

Substitute 1 for n1 , θ for θ1 and nR for n2 in above equation

θ2=ϕsin1(1sinθnR)=ϕsin1(sinθnR)

Write the expression for snell’s law,

n1sinθ1=n2sin(θ2)sin(θ1)=(n2sinθ2n1)θ1=sin1(n2sinθ2n1)

Here,

θ1 is deviation of red light from incidence light.

θ2 is angle of refraction for red light

n1 is the refractive index for air.

n2 is refractive index for red light

Substitute θ2=ϕsin1(sinθnR) for θ2 , 1 for n1 , θR for θ1 and for nR for n2 in above equation.

θR=sin1(nRsin(ϕsin1(sinθnR))1)=sin1(nRsin(ϕsin1(sinθnR)))

Write the expression for snell’s law for prism to calculate angle of refraction for violet light.

n1sinθ1=n2sin(ϕθ2)sin(ϕθ2)=(n1sinθ1n2)θ2=ϕsin1(n1sinθ1n2) (2)

Here,

n1 is refractive index for air.

θ1 is angle of incidence for violet light.

n2 is refractive index for violet light.

θ2 is the angle of refraction for violet light.

ϕ is the apex angle.

Substitute 1 for n1 , θ for θ1 and nV for n2 in equation (2).

θ2=ϕsin1(1sinθnV)=ϕsin1(sinθnV)

Write the expression for Snell's law.

n1sinθ1=n2sin(θ2)sin(θ1)=(n2sinθ2n1)θ1=sin1(n2sinθ2n1)

Here,

θ1 is deviation of violet light from incidence light.

θ2 is angle of refraction for violet light

n1 is the refractive index for air.

n2 is refractive index for violet light.

Substitute θ2=ϕsin1(sinθnV) for θ2 , 1 for n1 , θV for θ1 and for nV for n2 in above equation.

θV=sin1(nVsin(ϕsin1(sinθnV))1)=sin1(nVsin(ϕsin1(sinθnV)))

Write the expression for angular spread of visible light,

ω=θVθR

Here,

θV is deviation of violet light from visible light.

θR is the deviation of red light from visible light.

Substitute sin1(nVsin(ϕsin1(sinθnV))) for θV and sin1(nRsin(ϕsin1(sinθnR))) for θR in above equation.

ω=sin1(nVsin(ϕsin1(sinθnV)))sin1(nRsin(ϕsin1(sinθnR)))

Conclusion:

Therefore, the angular spread of visible light passing through a prism is sin1[nVsin(ϕsin1(sinθnV))]sin1[nRsin(ϕsin1(sinθnR))] .

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Chapter 35 Solutions

Physics for Scientists and Engineers, Technology Update (No access codes included)

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