JEE Advanced · Physics · 24. Ray Optics

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

A For this prism, the emergent ray at the second surface will be tangential to the surface when the angle of incidence at the first surface is $\left[\sin A \sqrt{4\left(\cos \frac{A}{2}\right)^2-1}-\cos A\right]$
B For the angle of incidence $i_{1} = A$ , the ray inside the prism is parallel to the base of the prism.
C At minimum deviation, the incident angle $i_{1}$ and the refracting angle $r_{1}$ at the first refracting surface are related by $r_{1} = (\frac{i_{1}}{2})$
D For this prism, the refractive index $μ$ and the angle of prism $A$ are related as $A = \frac{1}{2} \cos^{- 1} (\frac{μ}{2})$

Verified Solution

Answer & Solution

Correct Answer

(A) For this prism, the emergent ray at the second surface will be tangential to the surface when the angle of incidence at the first surface is $\left[\sin A \sqrt{4\left(\cos \frac{A}{2}\right)^2-1}-\cos A\right]$

Step-by-step Solution

Detailed explanation

i = e

(for minimum deviation)

r_{1} + r_{2} = A, r_{1} = r_{2}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Match List I with List II and select the correct answer using the codes given below the lists:

	$\text{List I}$		$\text{List II}$
a.	Boltzmann constant	p.	$\left[M L^2 T^{-1}\right]$
b.	Coefficient of viscosity	q.	$\left[M L^{-1} T^{-1}\right]$
c.	Planck constant	r.	$\left[M L T^{-3} K^{-1}\right]$
d.	Thermal conductivity	s.	$\left[M L^2 T^{-2} K^{-1}\right]$

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List - I	List - II
(P)	(1) Reaction with phenyl diazonium salt gives #ff0 dye.
(Q)	(2) Reaction with ninhydrin gives purple color and it also reacts with $FeCl _3$ to give violet color.
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(S)	(4) Lassiagne extract of the compound treated with dilute HCl followed by addition of aqueous $FeCl _3$ gives blood red color.
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	\(\text{List I}\)		\(\text{List II}\)
a.	Boltzmann constant	p.	\(\left[M L^2 T^{-1}\right]\)
b.	Coefficient of viscosity	q.	\(\left[M L^{-1} T^{-1}\right]\)
c.	Planck constant	r.	\(\left[M L T^{-3} K^{-1}\right]\)
d.	Thermal conductivity	s.	\(\left[M L^2 T^{-2} K^{-1}\right]\)

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

Step-by-step Solution

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