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Saturday, 31 October

JEE Main 2021 · PhysicsMultiple choiceSingle correctMediumMulti-step

JEE Main 22 July 2021, Shift 2, Physics Q3

Question 3 of 90 in this shift, Physics question 3 of 30, Section A.

A ray of light passes from a denser medium to a rarer medium at an angle of incidence ii. The reflected and refracted rays make an angle of 90∘90^\circ with each other. The angle of reflection and refraction are respectively r and r′'. The critical angle is given by :

The figure, in words

Hatched (shaded) block on top with a horizontal boundary line below it; a dashed/vertical normal line through the point of incidence. Incident ray comes from upper left down to the boundary point, labelled angle i with the normal; reflected ray goes up to the right, labelled angle r with the normal; refracted ray continues below the boundary, bending away from the normal toward the lower right, labelled angle r' with the normal below.
  1. (1)tan⁡−1(sin⁡i)\tan^{-1}(\sin i)
  2. (2)sin⁡−1(tan⁡r′)\sin^{-1}(\tan r')
  3. (3)sin⁡−1(tan⁡r)\sin^{-1}(\tan r)Official answer
  4. (4)sin⁡−1(cot⁡r)\sin^{-1}(\cot r)

Official answer

Option 3

NTA final key.

Chapter
Ray Optics and Optical Instruments
Topic
Refraction and Snell's Law
Idea tested
Total Internal Reflection

Same idea in other shifts

Asked 9× in all
  1. 7 Apr 2025, Shift 2 · Q42A transparent block A having refractive index μ=1.25\mu=1.25 is surrounded by another medium of refractive index μ=1.0\mu=1.0 as shown in figure.…MediumSingle correctHas a figure
  2. 8 Apr 2024, Shift 1 · Q43Critical angle of incidence for a pair of optical media is 45∘45^\circ. The refractive indices of first and second media are in the ratio:EasySingle correct
  3. 11 Apr 2023, Shift 1 · Q35The critical angle for a denser-rarer interface is 45∘45^\circ. The speed of light in rarer medium is 3×1083 \times 10^8 m/s. The speed of…EasySingle correct
  4. 25 Jun 2022, Shift 1 · Q44A light wave travelling linearly in a medium of dielectric constant 4, incidents on the horizontal interface separating medium with air.…MediumSingle correct
  5. 25 Jul 2021, Shift 1 · Q9A ray of laser of a wavelength 630 nm is incident at an angle of 30∘30^\circ at the diamond-air interface. It is going from diamond to air.…EasySingle correct
  6. 25 Jul 2021, Shift 2 · Q16A ray of light entering from air into a denser medium of refractive index 43\frac{4}{3}, as shown in figure. The light ray suffers total…MediumDiagram basedHas a figure
  7. 8 Jan 2020, Shift 1 · Q15The critical angle of a medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability…MediumSingle correct
  8. 9 Jan 2020, Shift 2 · Q17There is a small source of light at some depth below the surface of water (refractive index =43= \frac{4}{3}) in a tank of large cross…HardSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. This question needs a figure we do not reproduce; it is described in words above. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.