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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:

separate the red colour part from the green and blue colours

separateall all three colours from one another

not separate the three colours at all

separate the blue colour part front the red and green colours

Solution:

For total internal reflection, i > ic
Here i = 45°
sin i sin r = μ sin 45° > 1
μ > 1/√2 = 1.414
μred < 1.414
but μgreen > 1.414 and μviolet > 1.414.
Hence, green and violet will be totally internally reflected. Red will be refracted.