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Ray Optics and Optical Instruments · Question 57

JEE Main 2025 (Online) 29th January Morning ShiftMCQHard📈 Topic in 19% papers+4−1
1

At the interface between two materials having refractive indices n1 and n2, the critical angle for reflection of an em wave is 1C. The n2 material is replaced by another material having refractive index n3 such that the critical angle at the interface between n1 and n3 materials is 2C. If n3 > n2 > n1; n2n3 = 25 and 2C - 1C = 12, then 1C is :

  1. -1 ( 16n1 )
  2. -1 ( 13n1 )
  3. -1 ( 56n1 )
  4. -1 ( 23n1 )

Answer

Solution

Since n2 > n1 and n3 > n1, total internal reflection takes place for light going from n2 (or n3) into n1:

1C = n1n2, 2C = n1n3 = n1n2 n2n3 = 25 1C

2C - 1C = - 35 1C, which is negative and can never equal + 12.

Taking the magnitude, 35 1C = 12 1C = 56, i.e. 1C = -1 ( 56 ), which does not depend on n1.

None of the given options is correct; the question was awarded as bonus.

JEE Main 2025 (Online) 29th January Morning Shift

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2

A thin prism P1 with angle 4 made of glass having refractive index 1.54, is combined with another thin prism P2 made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism P2 in degrees is

  1. 1.5
  2. 16/3
  3. 3
  4. 4
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3

A hemispherical vessel is completely filled with a liquid of refractive index . A small coin is kept at the lowest point (O) of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point E (at the level of the vessel) is . [figure]

  1. 32
  2. 32
  3. 3
  4. 2
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4

A concave mirror produces an image of an object such that the distance between the object and image is 20 cm. If the magnification of the image is -3, then the magnitude of the radius of curvature of the mirror is :

  1. 3.75 cm
  2. 15 cm
  3. 7.5 cm
  4. 30 cm
JEE Main 2025 (Online) 28th January Evening Shift
5

In a long glass tube, mixture of two liquids A and B with refractive indices 1.3 and 1.4 respectively, forms a convex refractive meniscus towards A. If an object placed at 13 cm from the vertex of the meniscus in A forms an image with a magnification of -2, then the radius of curvature of meniscus is :

  1. 23 cm
  2. 43 cm
  3. 13 cm
  4. 1 cm
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