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Draw a ray diagram showing the path of a ray of light entering through a triangular glass prism. Deduce the expression for the refractive index of glass prism in terms of the angle of minimum deviation and angle of the prism. |
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Answer» Solution :Refraction of light rays through a prism has been shown in FIG. 9.77. Here `anglei` is the incidence angle at FIRST surface of prism and `anglee`is the angle of emergence from the second surface. `angler_(1)`and `angler_(2)`are the respective refraction angles at the two FACES and `angleinfty`is the angle of deviation. These angles are corelated as : `anglerr_(1) + angler_(2) = angleA`..........(i) and `anglei + anglee = angleA + angledelta`........(ii)  A graph showing variation in angle of deviation (8) with variation in angle of incidence (z) is shown in Fig. 9.78. As minimum deviation position corresponds to only one angle of incidence, it means that for minimum deviation position `anglei = anglee`and also `angler_(1) = angler_(2)`Thus, in minimum deviation position `=(A+D_(m))/2` and `2angler_(1) =A` or `angler_(1) = A/2` `therefore` Refractive INDEX of prism `n =(sin i)/(SINI r_(1)) = ((sin(A+D_(m))/2)/(sin A/2))` 
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