A right-angled glass prism is shown in the fi | vedclass

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(A) The prism is a right-angled triangle with angles $30^{\circ}, 60^{\circ}, 90^{\circ}$.When a ray of light is incident normally on face $AB$,it pas

Vedclass · Accepted Answer

$< \frac{3 \sqrt{3}}{4}$

Vedclass · Answer

(A) The prism is a right-angled triangle with angles $30^{\circ}, 60^{\circ}, 90^{\circ}$.When a ray of light is incident normally on face $AB$,it passes undeviated into the prism.It then strikes the hypotenuse face at an angle of incidence $i = 60^{\circ}$.For total internal reflection $(TIR)$ to occur at the hypotenuse face,the angle of incidence must be greater than the critical angle $C$,i.e.,$i > C$.Thus,$\sin(i) > \sin(C)$.Given $i = 60^{\circ}$,we have $\sin(60^{\circ}) > \frac{\mu_l}{\mu_{	ext{glass}}}$.$\frac{\sqrt{3}}{2} > \frac{\mu_l}{3/2}$.$\frac{\sqrt{3}}{2} > \frac{2 \mu_l}{3}$.$\mu_l Therefore,the refractive index of the liquid must be less than $\frac{3 \sqrt{3}}{4}$.

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