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Geometrical Optics question

2017 · Shift 1 · Q43
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Geometrical Optics question

2017 · Shift 1 · Q43

JEE AdvancedPhysicsGeometrical OpticsMultiple correct+4 / −1
For an isosceles prism of angle AAA and refractive index μ\muμ, it is found that the angle of minimum deviation δm=A.{\delta _m} = A.δm​=A. Which of the following options is/are correct?
  1. A
    For the angle of incidence i1=A,{i_1} = A,i1​=A, the ray inside the prism is parallel to the base of the prism
  2. B
    For this prism, the refractive index μ\muμ and the angle of prism AAA are related as A=12cos⁡−1(μ2)A = {1 \over 2}{\cos ^{ - 1}}\left( {{\mu \over 2}} \right)A=21​cos−1(2μ​)
  3. C
    At minimum deviation, the incident angle i1{i_1}i1​ and the refracting angle r1{r_1}r1​ at the first refracting surface are related by r1=(i1/2){r_1} = \left( {{i_1}/2} \right)r1​=(i1​/2)
  4. D
    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 i1=sin⁡−1[sin⁡A4cos⁡2A2−1−cos⁡A]{i_1} = {\sin ^{ - 1}}\left[ {\sin A\sqrt {4{{\cos }^2}{A \over 2} - 1} - \cos A} \right]i1​=sin−1[sinA4cos22A​−1​−cosA]
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