COLLEGE PHYSICS,VOLUME 1
COLLEGE PHYSICS,VOLUME 1
2nd Edition
ISBN: 9781319115104
Author: Freedman
Publisher: MAC HIGHER
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Chapter 23, Problem 114QAP
To determine

The angular separation between the red and blur portion of the spectrum that emerges from the prism

Expert Solution & Answer
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Answer to Problem 114QAP

The angular separation of blue and red color is 1.587°.

Explanation of Solution

Given info:

Each angle of prism = A=B=C=60° (since, prism is equilateral triangle)
Angle of incidence = i=60°

Refractive index of prism for red = nred=1.51

Refractive index of prism for blue = nblue=1.53

Formula used:

By Snell's law, following equation satisfy for refraction of light,
  n1Sini=n2Sinrhere, i and r are the angle of incidence and angle of refractionrespectively.

Calculation:

  COLLEGE PHYSICS,VOLUME 1, Chapter 23, Problem 114QAP In quadrilateral AQTR,
  AQT+TRA+RAQ+QTR=360o90o+90o+A+T=360osince, RAQ=A;QTR=TT=180oA.......(1)now, in ΔQTR,QTR+TRQ+RQT=180oT+r+r'=180o180oA+r+r'=180oA=r+r'........(2)

At the surface AB,
  n=sinisinrr=sin1( sinin).........(3)

Now, at the surface of AC,
  nsinr'=sini'i'=sin1(nsinr')i'=sin1(nsin(Ar))(from(2))i'=sin1(nsin( A sin 1 ( sini n )))........(4)(from(3))

From the geometry, the exterior angle is equal to the sum of opposite interior angle.

So, from the figure,
  δ=(ir)+(i'r')δ=(i+i')(r+r')δ=i+sin1(nsin( A sin 1 ( sini n )))Aδ=iA+sin1(nsin( A sin 1 ( sini n )))Forred,δred=iA+sin1(n redsin( A sin 1 ( sini n red )))

For blue,
  δblue=iA+sin1(n bluesin( A sin 1 ( sini n blue )))Now,Δθ=δblueδredΔθ=sin1(n bluesin( A sin 1 ( sini n blue )))sin1(n redsin( A sin 1 ( sini n red )))Δθ=sin1(1.53sin( 60 o sin 1 ( sin 60 o 1.53 )))sin1(1.51sin( 60 o sin 1 ( sin 60 o 1.51 )))Δθ=41.24748°39.66045°Δθ=1.587°

Conclusion:

Thus, the angular separation of red and blue color is 1.587°.

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Chapter 23 Solutions

COLLEGE PHYSICS,VOLUME 1

Ch. 23 - Prob. 11QAPCh. 23 - Prob. 12QAPCh. 23 - Prob. 13QAPCh. 23 - Prob. 14QAPCh. 23 - Prob. 15QAPCh. 23 - Prob. 16QAPCh. 23 - Prob. 17QAPCh. 23 - Prob. 18QAPCh. 23 - Prob. 19QAPCh. 23 - Prob. 20QAPCh. 23 - Prob. 21QAPCh. 23 - Prob. 22QAPCh. 23 - Prob. 23QAPCh. 23 - Prob. 24QAPCh. 23 - Prob. 25QAPCh. 23 - Prob. 26QAPCh. 23 - Prob. 27QAPCh. 23 - Prob. 28QAPCh. 23 - Prob. 29QAPCh. 23 - Prob. 30QAPCh. 23 - Prob. 31QAPCh. 23 - Prob. 32QAPCh. 23 - Prob. 33QAPCh. 23 - Prob. 34QAPCh. 23 - Prob. 35QAPCh. 23 - Prob. 36QAPCh. 23 - Prob. 37QAPCh. 23 - Prob. 38QAPCh. 23 - Prob. 39QAPCh. 23 - Prob. 40QAPCh. 23 - Prob. 41QAPCh. 23 - Prob. 42QAPCh. 23 - Prob. 43QAPCh. 23 - Prob. 44QAPCh. 23 - Prob. 45QAPCh. 23 - Prob. 46QAPCh. 23 - Prob. 47QAPCh. 23 - Prob. 48QAPCh. 23 - Prob. 49QAPCh. 23 - Prob. 50QAPCh. 23 - Prob. 51QAPCh. 23 - Prob. 52QAPCh. 23 - Prob. 53QAPCh. 23 - Prob. 54QAPCh. 23 - Prob. 55QAPCh. 23 - Prob. 56QAPCh. 23 - Prob. 57QAPCh. 23 - Prob. 58QAPCh. 23 - Prob. 59QAPCh. 23 - Prob. 60QAPCh. 23 - Prob. 61QAPCh. 23 - Prob. 62QAPCh. 23 - Prob. 63QAPCh. 23 - Prob. 64QAPCh. 23 - Prob. 65QAPCh. 23 - Prob. 66QAPCh. 23 - Prob. 67QAPCh. 23 - Prob. 68QAPCh. 23 - Prob. 69QAPCh. 23 - Prob. 70QAPCh. 23 - Prob. 71QAPCh. 23 - Prob. 72QAPCh. 23 - Prob. 73QAPCh. 23 - Prob. 74QAPCh. 23 - Prob. 75QAPCh. 23 - Prob. 76QAPCh. 23 - Prob. 77QAPCh. 23 - Prob. 78QAPCh. 23 - Prob. 79QAPCh. 23 - Prob. 80QAPCh. 23 - Prob. 81QAPCh. 23 - Prob. 82QAPCh. 23 - Prob. 83QAPCh. 23 - Prob. 84QAPCh. 23 - Prob. 85QAPCh. 23 - Prob. 86QAPCh. 23 - Prob. 87QAPCh. 23 - Prob. 88QAPCh. 23 - Prob. 89QAPCh. 23 - Prob. 90QAPCh. 23 - Prob. 91QAPCh. 23 - Prob. 92QAPCh. 23 - Prob. 93QAPCh. 23 - Prob. 94QAPCh. 23 - Prob. 95QAPCh. 23 - Prob. 96QAPCh. 23 - Prob. 97QAPCh. 23 - Prob. 98QAPCh. 23 - Prob. 99QAPCh. 23 - Prob. 100QAPCh. 23 - Prob. 101QAPCh. 23 - Prob. 102QAPCh. 23 - Prob. 103QAPCh. 23 - Prob. 104QAPCh. 23 - Prob. 105QAPCh. 23 - Prob. 106QAPCh. 23 - Prob. 107QAPCh. 23 - Prob. 108QAPCh. 23 - Prob. 109QAPCh. 23 - Prob. 110QAPCh. 23 - Prob. 111QAPCh. 23 - Prob. 112QAPCh. 23 - Prob. 113QAPCh. 23 - Prob. 114QAP
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