A $$semi-cylinder$$ made of transparent plastic has a refractive index n $$=$$ $$2$$ and a radius of R. There is a narrow incident light ray perpendicular to the flat side of the semi cylinder at d distance from the axis of symmetry.What can the maximum value of d be so that the light ray can still leave the other side of the semi cylinder?When the value of d chosen is such that TIR just takes place then time for which light remains inside the cylinder is:Distance d is now varied, so that the ray always emerges from the other side of the semi cylinder. What is the range of OB?

Question

A $$semi-cylinder$$ made of transparent plastic has a refractive index  n $$=$$ $$2$$ and a radius of R. There is a narrow incident light ray perpendicular to the flat side of the semi cylinder at d distance from the axis of symmetry.What can the maximum value of d be so that the light ray can still leave the other side of the semi cylinder?When the value of d chosen is such that TIR just takes place then time for which light remains inside the cylinder is:Distance d is now varied, so that the ray always emerges from the other side of the semi cylinder. What is the range of OB?

Infinity Learn · Accepted Answer

$$sin$$⁡θ$$C=12$$⇒θ$$C=45$$∘ ⇒$$d=R2Total$$ distance travel in the semi cylinder $$=22ROptical$$ path $$travel=(22R)$$×$$2=4R$$  time $$=4Rc$$  Range $$R2$$ to ∞

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