60. 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 :

60. 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 all the three colours from one another

(b) not separate the three colours at all

(c) separate the red colour part from the green and blue colours

(d) separate the blue colour part from the red and green colours

Answer :  (c) separate the red colour part from the green and blue colours

\(\sin i_c = \frac{1}{\mu}\)

\(\sin 45^\circ = \frac{1}{\mu} = \frac{1}{\sqrt{2}}\)

\(\mu = \sqrt{2} \approx 1.4\)

Red

\(\mu = 1.39\)

\(i_c\) higher than \(45^\circ\)

Since \(i = 45^\circ < i_c\), No TIR happens

Green

\(\mu = 1.44\)

\(i_c = 45^\circ\)

Since \(i = i_c\), Grazing surface

Blue

\(\mu = 1.47\)

\(i_c\) will be less than \(45^\circ\)

Since \(i = 45^\circ > i_c\), TIR will happen