A triangular medium has varying refracting index $$n=n0+ax$$, where x is the distance (in$$ $$cm) along $$x-axis$$ from origin and $$n0=43$$. A ray is incident normally on face OA at the $$mid-point$$ of OA. The range of a so that light does not escape through face AB when it falls first time on the face AB (OA$$ $$=$$ $$4$$ cm, OB $$=$$ $$3$$ cm and AB $$=$$ $$5$$ $$cm): (Surrounding$$ medium is $$air)

Question

A triangular medium has varying refracting index $$n=n0+ax$$, where x is the distance (in$$ $$cm) along $$x-axis$$ from origin and $$n0=43$$. A ray is incident normally on face OA at the $$mid-point$$ of OA. The range of a so that light does not escape through face AB when it falls first time on the face AB (OA$$ $$=$$ $$4$$ cm, OB $$=$$ $$3$$ cm and AB $$=$$ $$5$$ $$cm): (Surrounding$$ medium is $$air)

Infinity Learn · Accepted Answer

Clearly, $$PM=32cmFor$$ TIR, $$370$$>C $$or)370$$> $$sin$$$$-2(3/2)370$$>$$sin$$−$$1$$⁡$$1n0+a(3/2)35$$>$$1n0+3a23n0+9a2$$>$$59a2$$>$$1a$$>$$29$$

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