An equilateral prism ABC is placed in air with its base side BC lying horizontally along x-axis as shown in figure. A ray given by 
z + x = 10 is incident at a point P on face AB of prism.
(i) Find the value of μ for which the ray grazes the face AC –
Text Solution
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Ans.
(i)
Sol. 
z + x = 10
z = 
+ 
Slope = 
tan θ = 
θ = – 30º
Thus ray is incident normally on the face AB. Thus angle of incidence on face AC is 60º. For grazing μ sin 60º = 1 × sin 90º
μ = 
(ii)
Sol. For μ = 
the ray get internally reflect.
∴ The ray is normal on face BC. Hence finally refracted ray is parallel to z axis.
(iii)
Sol. If BC is silvered, the ray will retrace its path. Hence equation of ray coming out of the prism is 
z + x = 10
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