For an isosceles prism of angle A and refractive index μ , it is found that the angle of minimum deviation δ$$m=A$$. Which of the following options $$is/are$$ correct?

Question

For an isosceles prism of angle A and refractive index μ , it is found that the angle of minimum deviation  δ$$m=A$$. Which of the following options $$is/are$$ correct?

Infinity Learn · Accepted Answer

δ$$m=A$$ & μ$$=$$$$sin$$⁡$$A+$$δ¯$$m2sin$$⁡$$A/2$$⇒μ$$=$$$$sin$$⁡Asin⁡$$A/2$$⇒μ$$=2sin$$⁡$$A/2cos$$⁡$$A/2sin$$⁡$$A/2=2cos$$⁡$$A/2$$⇒$$cos$$⁡$$A/2=($$μ$$/2)$$⇒(A/2)=$$$$cos$$−$$1$$⁡$$($$μ$$/2)⇒$$A=2cos$$−$$1$$⁡$$($$μ$$/2)$$ (D) is not correct. δ$$m=i1+i2$$−A⇒$$i1+i2=2A$$ and $$i1=i2=ASo$$ option A is correct.$$r1=r2$$ and μ$$=$$$$sin$$⁡$$i1sin$$⁡$$r12cos$$⁡$$A/2=$$$$sin$$⁡Asin⁡$$r1$$⇒$$sin$$⁡$$r1=2sin$$⁡$$A/2cos$$⁡$$A/22cos$$⁡$$A/2$$⇒$$r1=A/2=i1/2$$ option (B) is correct Emergent ray tangential to the surface $$meansi2=90$$∘⇒$$r2=C$$ (critical$$ $$angle) $$r1=(A$$−$$C)$$μ$$=$$$$sin$$⁡$$i1sin$$⁡$$r1sin$$⁡$$i1=$$μ$$sin$$⁡$$r1=2cos$$⁡$$A/2$$[$$sin$$⁡(A$$−$$C)]$$=2cos$$⁡$$A/2($$$$sin$$⁡Acos⁡C−$$cos$$⁡Asin⁡$$C)=2cos$$⁡$$A/2sin$$⁡$$A1$$−$$sin2$$⁡C−$$cos$$⁡$$A1$$μ$$=2cos$$⁡$$A/2sin$$⁡$$A1$$−$$1$$μ$$2$$−$$cos$$⁡$$A1$$μ$$=2cos$$⁡$$A/2sin$$⁡$$A1$$−$$14cos2$$⁡$$A/2$$−$$cos$$⁡$$A12cos$$⁡$$A/2=2cos$$⁡$$A/2sin$$⁡$$A4cos2$$⁡$$A/2$$−$$12cos$$⁡$$A/2$$−$$cos$$⁡$$A12cos$$⁡$$A/2=$$$$sin$$⁡$$A4cos2$$⁡$$A/2$$−$$1$$−$$cos$$⁡A⇒$$i1=$$$$sin$$−$$1$$⁡$$sin$$−$$1$$⁡$$A4cos2$$⁡$$A/2$$−$$1$$−$$cos$$⁡AOption C is correct

For an isosceles prism of angle A and refractive index μ , it is found that the angle of minimum deviation δm=A. Which of the following options is/are correct?

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