The index of refraction for a certain kind of glass is 1.649for violet light and

Question

The index of refraction for a certain kind of glass is 1.649for violet light and 1.614 for red light. A ray of violet light anda ray of red light are both incident on this glass from air andboth have the same refraction angle of 31.03o. What isthe difference between the angles of incidence of the tworays?
I used snell's law. In the end I had sin-1(nviolet/2*1.00) -sin-1(nred/2*1.00) The difference was 1.74 degrees but that was incorrect pleasehelp The index of refraction for a certain kind of glass is 1.649for violet light and 1.614 for red light. A ray of violet light anda ray of red light are both incident on this glass from air andboth have the same refraction angle of 31.03o. What isthe difference between the angles of incidence of the tworays?
I used snell's law. In the end I had sin-1(nviolet/2*1.00) -sin-1(nred/2*1.00) The difference was 1.74 degrees but that was incorrect pleasehelp

Explanation / Answer

Given :           Refractive index of red   (nr ) = 1.614           Refractive index of violet (nv ) = 1.649 For Red light :           From Snell's law :                  n1  ( sin1)r = nr ( sin2 )r         or       (sin2 )r      = ( n1 / nr ) * (sin1)r     -----------(1) For Violet light :             FromSnell's law :                  n1  ( sin1)v = nv ( sin2 )v         or       (sin2 )v     = ( n1 / nv ) * (sin1)v     -----------(1) Given that Both colorsenter the glass at the same angle of refraction.                  i.e.  (sin2 )r   =    (sin2 )v Hence from (1) and (2)                             n1  ( sin1)v = nv ( sin2 )v         or       (sin2 )v     = ( n1 / nv ) * (sin1)v     -----------(1) Given that Both colorsenter the glass at the same angle of refraction.                  i.e.  (sin2 )r   =    (sin2 )v Hence from (1) and (2)                  ( n1 / nr) * (sin1)r  =    ( n1 / nv ) * (sin1)v         or         (sin1)r /  nr =    (sin1)v /nv         or         (sin1)v        =     (sin1)r  * (  nv /  nr )                                          =    (sin 31.03 ) * ( 1.649 / 1.614)                                           =  0.526665                        (1)v     =  sin-1 (0.526665)                                          =   31.78 degree Hope this helps u!           

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