Modern Physics for Scientists and Engineers
Modern Physics for Scientists and Engineers
4th Edition
ISBN: 9781133103721
Author: Stephen T. Thornton, Andrew Rex
Publisher: Cengage Learning
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Chapter 2, Problem 34P
To determine

Difference in the speed of the light flowing along with the direction of flow of water and opposite to the direction of the flow of the water.

Expert Solution & Answer
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Answer to Problem 34P

Difference in the speed of the light flowing along with the direction of flow of water and opposite to the direction of the flow of the water is 4.35 m / s.

Explanation of Solution

Write the velocity of the light flowing in the direction of flow of water. Thus,

u1=u+v1+uv/c2=c/n+v1+v/nc=cn(1+nvc)(1+vnc)                                                                                                      

Where, v is the velocity of the flow of the water, n is the index refraction of the water, c is the speed of the light and u=cn is the speed of the light in the medium with index refraction n.

Further simplify the above equation by using binomial expansion because vc. Thus,

u1=cn(1+nvc)(1+vnc)1              =cn(1+nvc)(1vnc)cn (1vnc+nvcv2c2)                                                                        

Because vc, therefore, v2c20, simplify the above equation. Thus,

u1cn (1vnc+nvc)                                                                                (I)

Similarly, write the velocity of the light flowing in opposite direction of flow of water. Thus,

u2=u+(v)1+u(v)/c2=c/nv1v/nc=cn(1nvc)(1vnc)                                                                                                      

Further simplify the above equation by using binomial expansion because vc. Thus,

u2=cn(1nvc)(1vnc)1              =cn(1nvc)(1+vnc)cn (1+vncnvcv2c2)                                                                        

Because vc, therefore, v2c20, simplify the above equation. Thus,

u2cn (1+vncnvc)                                                                                (II)

Subtract equation (I) from equation (II) to get the difference in the speed of the light flowing along with the direction of flow of water and opposite to the direction of the flow of the water. Thus,

Δu=u1u2cn (1vnc+nvc)cn (1+vncnvc)=   cn(1vnc+nvc1vnc+nvc)=cn(2nvc2vnc)

Further simplify the above equation. Thus,

     Δu=2v(11n2)  

Substitute v=5 m / s E and n=1.33 in the above equation. Thus,

     Δu=2×5 m / s(111.332)=10 m / s×0.43464.35 m / s  

Conclusion:

Therefore, difference in the speed of the light flowing along with the direction of flow of water and opposite to the direction of the flow of the water is 4.35 m / s.

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Chapter 2 Solutions

Modern Physics for Scientists and Engineers

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