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CBSE Class 12-science Answered

a 60° prism has a refractive index of 1.5 Calculate the angle of incidence for minimum deviation , the angle of emergence of light at maximum deviation and angle of maximum deviation.
Asked by Saranya | 14 Jun, 2018, 10:31: PM
answered-by-expert Expert Answer
The formula relating refractive index, Angle of prism and angle of minimu deviation is 
 
begin mathsize 12px style mu space equals space fraction numerator sin open square brackets open parentheses A plus D subscript m close parentheses divided by 2 close square brackets over denominator sin open square brackets A divided by 2 close square brackets end fraction end style , where μ is the refractive index, A is angle of prism and Dm is minimum angle of deviation
by substituting A = 60º, μ=1.5 and solving for Dm we get, Dm = 37.2°.
 
Maximum angle of deviation occurs when incident angle i is 90°. 
As shown in figure, angle of deviation δ is given by , δ = i + e - A ................(1)
 
also we have,     r + r' = A ........................(2)
 
for maximum angle of deviation, begin mathsize 12px style mu space equals space fraction numerator 1 over denominator sin space r end fraction space space semicolon space sin space r space equals space fraction numerator 1 over denominator 1.5 space end fraction space space semicolon space h e n c e space r space equals space 41.8 degree end style
from eqn.(2), r' = A-r = 60 - 41.8 = 18.2º
 
to get angle of emergence e, we have

 begin mathsize 12px style mu space equals space fraction numerator sin space e over denominator sin space r apostrophe end fraction space semicolon space sin space e space equals space mu cross times space sin space r apostrophe space equals space 1.5 cross times sin left parenthesis 18.2 right parenthesis space equals space 0.4685 space h e n c e space e space equals space 27.94 degree end style
 
from eqn.(1), we get maximum angle of deviation, δ = 90+27.94-60 = 57.94 º
Answered by Thiyagarajan K | 15 Jun, 2018, 12:10: PM

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