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Geometrical Optics question

2023 · 30 Jan · Shift 2 · Q53
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  5. /2023 · 30 Jan · Shift 2 · Q53

Geometrical Optics question

2023 · 30 Jan · Shift 2 · Q53

JEE MainPhysicsGeometrical OpticsMCQ+4 / −1
A thin prism P1P_1P1​ with an angle 6∘6^{\circ}6∘ and made of glass of refractive index 1.541.541.54 is combined with another prism P2P_2P2​ made from glass of refractive index 1.721.721.72 to produce dispersion without average deviation. The angle of prism P2P_2P2​ is
  1. A
    4.5∘4.5^{\circ}4.5∘
  2. B
    7.8∘7.8^{\circ}7.8∘
  3. C
    1.3∘1.3^{\circ}1.3∘
  4. D
    6∘6^{\circ}6∘
View written solutionFree

Correct answer: A

  1. Condition for dispersion without average deviation

For a thin prism, the deviation is

δ=(μ−1)A\delta = (\mu-1)Aδ=(μ−1)A

where μ\muμ is the refractive index and AAA is the prism angle.

If two thin prisms are combined to produce dispersion without average deviation, then their net mean deviation must be zero.

So, taking the prisms in opposite orientation,

(μ1−1)A1=(μ2−1)A2(\mu_1-1)A_1=(\mu_2-1)A_2(μ1​−1)A1​=(μ2​−1)A2​
  1. Substitute the given values

For prism P1P_1P1​:

μ1=1.54,A1=6∘\mu_1=1.54, \quad A_1=6^\circμ1​=1.54,A1​=6∘

For prism P2P_2P2​:

μ2=1.72,A2=?\mu_2=1.72, \quad A_2=?μ2​=1.72,A2​=?

Thus,

(1.54−1)(6∘)=(1.72−1)A2(1.54-1)(6^\circ)=(1.72-1)A_2(1.54−1)(6∘)=(1.72−1)A2​ 0.54×6=0.72 A20.54\times 6=0.72\,A_20.54×6=0.72A2​ 3.24=0.72A23.24=0.72A_23.24=0.72A2​ A2=3.240.72=4.5∘A_2=\frac{3.24}{0.72}=4.5^\circA2​=0.723.24​=4.5∘
  1. Match with the options
A2=4.5∘A_2=4.5^\circA2​=4.5∘

So the correct option is A.

  1. Verification with stored answer

Stored correct answer: A

Our derived answer: A

They match.

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