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Wave Optics

Question
CBSEENPH12039473

In an experiment for determination of refractive index of glass of a prism by i− δ, plot, it was found that a ray incident at angle 35o, suffers a deviation of 408 and that it emerges at angle 79o ⋅ Ιn that case which of the following is closest to the maximum possible value of the refractive index?

  • 1.5

  • 1.6

  • 1.7

  • 1.8

Solution

A.

1.5

C.

1.7

If μ is the refractive index of the material of prism, the from shell's law
straight mu space equals space fraction numerator sin space straight i over denominator sin space straight r end fraction space equals space fraction numerator sin space left parenthesis straight A space plus straight delta subscript straight m right parenthesis divided by 2 over denominator sin space straight A divided by 2 end fraction space space left parenthesis straight i right parenthesis
Where space straight A space is space angle space of space prism space and space straight delta subscript straight m space is space minimum space deviation space through space prism
Given comma space straight i space equals space 35 to the power of straight o comma space straight delta space equals space 40 to the power of straight o comma space straight e space equals space 79 to the power of straight o
so comma space angle space of space deviation space by space straight a space glass space prism comma
straight delta space equals space straight i space plus space straight e minus space straight A
40 to the power of straight o space equals space 35 to the power of straight o space plus 79 to the power of straight o minus space straight A
straight i. straight e space angle space of space prism space rightwards double arrow space straight A space equals space 74 to the power of straight o
So space angle space of space deviation space by space straight a space glass space prism
straight delta space equals space straight i space plus space straight e minus straight A
rightwards double arrow space 40 to the power of straight o space equals space 35 to the power of straight o space plus 79 to the power of straight o minus space straight A
straight i. straight e space angle space of space prism space rightwards double arrow space straight A space equals space 74 to the power of straight o
let space us space put space straight mu space equals space 15 space in space eq space left parenthesis straight i right parenthesis space we space get
1.5 space equals space fraction numerator sin open parentheses begin display style fraction numerator straight A space plus straight delta subscript min over denominator 2 end fraction end style close parentheses over denominator Sin space straight A divided by 2 end fraction
1.5 space equals space fraction numerator sin open parentheses begin display style fraction numerator 74 to the power of straight o space plus straight delta subscript min over denominator 2 end fraction end style close parentheses over denominator Sin 37 to the power of straight o end fraction
0.9 space equals space sin space open parentheses 37 to the power of o space plus delta subscript m i n end subscript over 2 close parentheses left parenthesis therefore space sin space 37 to the power of straight o space equals space 0.6 right parenthesis
sin space 64 to the power of straight o space equals space sin space open parentheses 37 to the power of straight o space plus straight delta subscript min over 2 close parentheses space left parenthesis therefore space sin space 64 to the power of straight o space equals space 0.9 right parenthesis
37 to the power of o space plus delta subscript m i n end subscript over 2 space equals space 64 to the power of straight o space rightwards double arrow straight delta subscript min space equals space 54 to the power of straight o space
This angle is greater than the 40o and deviation angle already given. For greaterμ deviation will be even higher. Hence μ of the given prism should be lesser than 1.5. Hence, the closest option will be 1.5

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