A parallel beam of light falls on a quarter cylinder of radius $$9$$ cm, as shown in figure (A). Refractive index of the material of the cylinder is $$3$$ . Maximum value of OP (in$$ cm $$), as shown in figure (B), so that rays don’t suffer TIR at the curved surface is (consider$$ refractive index of surrounding medium equal to $$1)

Question

A parallel beam of light falls on a quarter cylinder of radius $$9$$ cm, as shown in figure (A). Refractive index of the material of the cylinder is $$3$$ . Maximum value of OP (in$$ cm $$), as shown in figure (B), so that rays don’t suffer TIR at the curved surface is (consider$$ refractive index of surrounding medium equal to $$1)

Infinity Learn · Accepted Answer

Let say OP $$=$$ x and critical angle is formed at A.Applying Snell's Law at P,$$1sin600=3sinr$$​⇒$$r=300$$∠$$PAO=r1=critical$$ angle⇒$$sinr1=13$$ΔOPA,using Lami's Theorem $$sinr1x=sin90+30R$$⇒$$x=2R3=6cm$$

Total internal reflection - Ray optics and optical instruments

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Total internal reflection - Ray optics and optical instruments

Remember concepts with our Masterclasses.

Let say OP = x and critical angle is formed at A.Applying Snell's Law at P,1sin600=3sinr​⇒r=300∠PAO=r1=critical angle⇒sinr1=13ΔOPA,using Lami's Theorem sinr1x=sin90+30R⇒x=2R3=6cm

Ready to Test Your Skills?

free study material