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explain prism formula



25-Sep-2017 7:24 PM
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Answers (2)


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Let  A = angle of prism

          i= angle of incident

        e = angle of emerging

         k=angle of deviation   

     r1&r2=angle of refraction

         u=refractive index of the prism

From  quadrilateral APNQ

           A+N=180 -  (1)

From   triangle PNQ

           N+r1+r2=180-  (2)

From  (1)&(2)

           A=r1+r2-   (3)

By Snell's law

           sin i= u sin r1

           &  u sinr2=sin e

For  Snell's angle i.e, r1 & r2

         ( i = ur1 &  e = ur2 ) -   (4)

From  triangle PQD

            k= i-r1+e- r2

          = (u-1)r1 + ( u- r2)  since [4]

          = ( u-1) ( r1- r2)

          =  k = ( u-1)A   since (3)

 



25-09-2017 19:46
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How come that quadrilateral is cyclic



26-09-2017 08:15
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