Optics 4 Question 13
13. A beam of light consisting of red, green and blue colours is incident on a right-angled prism. The refractive indices 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 from the green and blue colours
(b) separate the blue colour from the red and green colours
(c) separate all the three colours from one another
(d) not separate even partially any colour from the other two colours.
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Solution:
- The colours for which $i>\theta _c$, will get total internal reflection $: i>\theta _c$ or $\sin i>\sin \theta _c$
or $\sin 45^{\circ}>\frac{1}{\mu}$ or $\frac{1}{\sqrt{2}}>\frac{1}{\mu}$
or for which $\mu>\sqrt{2}$ or $\mu>1.414$
Hence, the rays for which $\mu>1.414$ will get TIR.
For green and blue $\mu>1.414$, so they will suffer TIR on face $A C$. Only red comes out from this face.
