A planar structure of length L and width W is made of two different optical media of refractive indices $$n1=1.5$$ and $$n2=1.44$$ as shown in figure. If LW, a ray entering from end AB will emerge from end CD only if the total internal reflection condition is met inside the structure. For $$L=9.6m$$, if the incident angle θ is varied, the maximum time taken by a ray to exit the plane CD is t×$$10$$−$$9$$ s, where t $$is___$$

Question

A planar structure of length L and width W is made of two different optical media of refractive indices $$n1=1.5$$ and $$n2=1.44$$ as shown in figure. If  L>>W, a ray entering from end AB will emerge from end CD only if the total internal reflection condition is met inside the structure. For  $$L=9.6m$$, if the incident angle θ is varied, the maximum time taken by a ray to exit the plane CD is t×$$10$$−$$9$$ s, where t $$is___$$

Infinity Learn · Accepted Answer

$$sin$$⁡$$C=xd=n2n1$$⇒$$2425=xd$$⇒$$d=25x24$$→ distance travelled by light ray $$=2524$$×$$9.6=10m$$ Time taken by ray to travel $$=d$$ speed in med⁡$$n1$$⇒ time $$=10C1.5=1.5$$×$$103$$×$$108=5$$×$$10$$−$$8s=50$$×$$10$$−$$9s$$

Total internal reflection - Ray optics and optical instruments

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Total internal reflection - Ray optics and optical instruments

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sin⁡C=xd=n2n1⇒2425=xd⇒d=25x24→ distance travelled by light ray =2524×9.6=10m Time taken by ray to travel =d speed in med⁡n1⇒ time =10C1.5=1.5×103×108=5×10−8s=50×10−9s

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