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.

Options

A. not separate the three colours at all
B. separate the red colour part from the green and blue colours
C. separate the red colour part from the red and green colours
D. separate all the three colours from one another

Answer

B

Explanation

As been of light is incident normally on the dace AB of the right angled prism ABC, so no refraction occurs at face AB and it passes straight and Strikes the face AC at an angle of incidence `i=45^(@)` .
For total reflection to take place at face AC,
`igti_(c)orsinigtsini_(c)`
where `i_(c)` is the critical angle.
But as here `i=45^(@)` and `sini_(c)=(1)/(mu)`
`:.sin45^(@)gt(1)/(mu)"or"(1)/(sqrt(2))gt(1)/(mu) "or" mu gtsqrt(2)=1.414`
As `mu_("red")(=1.39)ltmu(=1.414)` while `mu_("green")(=1.44)` and `mu_("blue")(=1.47)gtmu(=1.414), ` so only red colour will be transmitted through face AC while green and blue colours will suffer total internal reflection. So the prism will separate red colour from the green and blue colours as shown in the following figure.