Prism formula

 

 

1) consider a prism ABC


2) WX ray incidents on the AB face at X position, after refraction, the ray passes through the prism and strikes at Y position of the AC face.


3) Suppose the incident angle at X is i1 and refracted angle at X is r1.


4) Now when the ray strikes at Y making an incident angle r2 at Y and refracted at Y along the YZ direction.


5) At Y position the refracted angle is i2 as shown in the diagram.


6) Now two normal at X & Y were drawn and they meet at Q.



7) Now when WX incident ray & final YZ refracted ray expand they meet at R position and making an angle  which is called angle of deviation.




8) Now from AXQY quadrilateral,






Therefore 






9) from 






therefore   




So, r1 + r2 =  <A  ……..  9.71




10) from  






Where d is the angle of deviation.



11) it is found the angle of deviation is minimumwhen

 



Or              i1   =   i2

               (Which means)

 





12) when    i1   =   i2    happens 


 r1   =   r2    will also happen, 



Now say  r1   =   r2   =  r



Now  from 9.71

r1   +  r2    = A



So,     2 r = A







13) Now say     i1   =   i2   =  i   (say)


Then from   9.78  , for 

minimum deviation,




we get that

  






14) Now from Snell’s Law:

Ifis the refractive index of the prism material then




On putting the value of i & r




Which is called the prism formula.