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.
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 the blue colour part from the red and green colours
B.
separate all the three colours from one another
C.
not separate the three colours at all
D.
separate the red colour part from the green and blue colours
Answer :
separate the red colour part from the green and blue colours
Solution :
For refractive index of a index,
$$\mu = \frac{1}{{\sin {i_c}}} = \frac{1}{{\sin {{45}^ \circ }}} = \sqrt 2 $$
$$\eqalign{ & {\text{As,}}\,\,{\mu _{{\text{red}}}} = 1.39,\,{\mu _{{\text{green}}}} = 1.44,\,{\mu _{{\text{blue}}}} = 1.47 \cr & \therefore \left( {{\mu _{{\text{red}}}} = 1.39} \right) < \mu ,{\mu _{{\text{green}}}} > \mu ,\,{\mu _{{\text{blue}}}} > \mu \cr} $$
Thus, only red colour do not suffer total internal reflection.
For refractive index of a index,
$$\mu = \frac{1}{{\sin {i_c}}} = \frac{1}{{\sin {{45}^ \circ }}} = \sqrt 2 $$
$$\eqalign{ & {\text{As,}}\,\,{\mu _{{\text{red}}}} = 1.39,\,{\mu _{{\text{green}}}} = 1.44,\,{\mu _{{\text{blue}}}} = 1.47 \cr & \therefore \left( {{\mu _{{\text{red}}}} = 1.39} \right) < \mu ,{\mu _{{\text{green}}}} > \mu ,\,{\mu _{{\text{blue}}}} > \mu \cr} $$
Thus, only red colour do not suffer total internal reflection.
