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Question

A beam of light consisting of red, green and blue colours is incident on a right-angled prism. The refractive index of the material of the prism for the above red, green and blue wavelengths are 1.39,1.44 and 1.47 respectively. The prism will


A
Separate the red colour part from the green and blue colours
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B
Separate the blue colour part from the red and green colours
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C
Separate all the three colours from one another
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D
Not separate the three colours at all
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Solution

The correct option is A Separate the red colour part from the green and blue colours
Since the beam of light rays is incident normally at the surface AB, it will reach undeviated at the surface AC.


From geometry, the angle of incidence at AC is, i=45
For red colour,
ic=sin1(μrμd)
ic=sin1(11.39)
ic=sin1(0.72)46.1 ..........(1)
For green colour,
ic=sin1(11.44)
ic=sin1(0.69)43.6 ..........(2)
For blue colour,
ic=sin1(11.47)
ic=sin1(0.68)42.8 ..........(3)
From (1), (2) and (3), we can see that, for red colour, i<ic, and for green and blue colour, i>ic.
Thus, green and blue colour will suffer total internal reflection while red will emerge out and hence get separated from green and blue colours.
Tip: You don't need to learn or find the exact sin values. Just remember sin45=0.707 and you can compare the others relatively.

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