A beam of light consisting of red,green,and b | vedclass

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(A) For total internal reflection $(TIR)$ to occur at the hypotenuse face,the angle of incidence $i$ must be greater than the critical angle $i_{c}$.F

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separate part of the red color from the green and blue colors.

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(A) For total internal reflection $(TIR)$ to occur at the hypotenuse face,the angle of incidence $i$ must be greater than the critical angle $i_{c}$.From the geometry of the right-angled prism,the light enters normally to the first face and strikes the hypotenuse at an angle of incidence $i = 45^{\circ}$.The condition for $TIR$ is $\sin i > \sin i_{c}$,where $\sin i_{c} = \frac{1}{\mu}$.Thus,$\sin 45^{\circ} > \frac{1}{\mu}$,which implies $\frac{1}{\sqrt{2}} > \frac{1}{\mu}$,or $\mu > \sqrt{2} \approx 1.414$.Comparing the given refractive indices:For red: $\mu_{red} = 1.39 For green: $\mu_{green} = 1.44 > 1.414$ (Undergoes $TIR$).For blue: $\mu_{blue} = 1.47 > 1.414$ (Undergoes $TIR$).Since red light is refracted and green and blue light undergo total internal reflection,the red color is separated from the green and blue colors.

$A$ beam of light consisting of red,green,and blue colors is incident on a right-angled prism as shown. The refractive indices of the material of the prism for red,green,and blue wavelengths are $1.39, 1.44$,and $1.47$ respectively. The prism will:

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