question_answer

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 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) none of these

Correct Answer: A

Solution :

The colours for which \[i\,\,>\,\,{{\theta }_{c}}\], will get total internal reflection \[i\,\,>\,\,{{\theta }_{c}}\] \[or\,\,sin\,\,\,i\,\,>\,\sin \,\,{{\theta }_{c}}\] \[or\,\,\sin \,\,45{}^\circ \,\,>\,\,\,1/\mu \] \[\,or\,\,\,\,\frac{1}{\sqrt{2}}>\frac{1}{\mu }\] \[or\,\,for\,\,which\,\,\mu \,\,>\sqrt{2}\,\,\,\,\,or\,\,\,\,\mu >1.414.\] 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 AC only red comes out from this face.