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2015-05-14T17:08:42+05:30

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The emerging ray in air contains only yellow, orange and red because if green is just totally internally reflected, then violet,indigo,blue are also totally internally reflected.
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2015-05-16T21:32:27+05:30

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See diagram.

Since we are talking of total internal reflection, the light ray is incident from glass medium on to the interface towards air.  Inside the glass the light is white light - consisting of VIBGYOR colors.

       1 / μ  = Sin  i  / Sin  r
           here  i = angle of incidence = same for all colors.
             μ = refractive index of glass wrt air

 Thus for each color,    Sin i = (1/ μ) * Sin r    = constant
                   r = 90 deg. for  i = C = critical angle

    critical angle for total internal reflection C = Sin⁻¹ (1/μ) 
 
    We know that in a glass prism when white light is dispersed into seven colors, the violet rays bends most. and red color bends less.  So angle of refraction for violet is the least.  Hence, the refractive index for the violet rays is the highest and that for the red rays is the least.

Now, coming back to our exercise :
     So critical angle for violet rays will be smallest.  Critical angle for red rays will be highest.    If the green light is just totally internally reflected then,  violet, Indigo, Blue are also reflected totally internally, as their critical angles are less than that of green light rays.

The emerging ie.,  refracted rays contain only:  Yellow, Orange, and Red colors.

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