# 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: Option 1) separate all the three colours from one another Option 2) not separate the three colours at all Option 3) separate the red colour part from the green and blue colours Option 4) separate the blue colour part from the red and green colours

As we learnt in

Critical angle -

$\sin c$ = Refractive index of rarer medium / Refractive index of denser medium

- wherein

When angle of incidence of a travelling from a dence medium to rarer medium is greater than critical angle, no refraction occurs.

angle of incidence at surface AC= $45^{\circ}$

Critical Angle of incidence

$sin\ c=\frac{1}{\mu}$

For red $\mu_r=1.39$

For green $\mu_g=1.44$

For blue $\mu_b=1.47$

Since refractive index of green and blue is greater than $\sqrt{2}$ and hence their critical angles are less than $45^{\circ}$

So green and blue will be completely reflected while red will emerge out of prism. Hence red will be separated from green and blue.

Option 1)

separate all the three colours from one another

Option 2)

not separate the three colours at all

Option 3)

separate the red colour part from the green and blue colours

Option 4)

separate the blue colour part from the red and green colours

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