For a glass prism of refractive index 1.5 the angle of minimum deviation is equal to angle of prism . What is the angle of prism.
What is the relation between angle i and angle r if the angle of deviation is minimum.

Asked by P S Lakshmi | 5th Mar, 2015, 09:47: PM

Expert Answer:

Given refractive index, μ = 1.5
 
begin mathsize 14px style Let space straight delta subscript straight m space be space the space angle space of space minimum space deviation. Given space Angle space of space prism comma space straight A space equals straight delta subscript straight m space We space know space that space straight mu space equals fraction numerator sin space left parenthesis begin display style fraction numerator straight A plus straight delta subscript straight m space over denominator 2 end fraction end style right parenthesis over denominator sin space open parentheses begin display style straight A over 2 end style close parentheses end fraction Substituting space comma we space get colon 1.5 space equals fraction numerator sin space left parenthesis begin display style fraction numerator straight A plus straight A space over denominator 2 end fraction end style right parenthesis over denominator sin space open parentheses begin display style straight A over 2 end style close parentheses end fraction 1.5 space equals fraction numerator sin space 2 left parenthesis begin display style fraction numerator straight A space over denominator 2 end fraction end style right parenthesis over denominator sin space open parentheses begin display style straight A over 2 end style close parentheses end fraction equals fraction numerator 2 space sin space begin display style straight A over 2 end style cos begin display style straight A over 2 end style begin display style blank end style over denominator sin space open parentheses begin display style straight A over 2 end style close parentheses end fraction 1.5 space equals 2 cos straight A over 2 0.75 space equals cos straight A over 2 straight A over 2 equals cos to the power of negative 1 end exponent open parentheses 0.75 close parentheses  straight A over 2 equals 41 degree straight A equals 82 degree end style
 
At the angle of minimum deviation, 2i - 2r =δmin

Answered by Jyothi Nair | 6th Mar, 2015, 11:02: PM

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