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A light ray entering a… (Class 12 Physics SQP 2024-25, Q27)

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PhysicsCBSE Class 12 · Sample paper, session 2024-25 · 3 marks · Short answer

CBSE Class 12 Physics sample paper 2024-25: question 27

From the official CBSE sample question paper for 2024-25, section C, question 27, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q27 · 3 marks · Short answerRay Optics and Optical Instruments

A light ray entering a right-angled prism undergoes refraction at the face AC as shown in Fig. 1.
(I) What is the refractive index of the material of the prism in Fig. 1?
(II) (a) If the side AC of the above prism is now surrounded by a liquid of refractive index , as shown in Fig. 2, determine if the light ray continues to graze along the interface AC or undergoes total internal reflection or undergoes refraction into the liquid.
(b) Draw the ray diagram to represent the path followed by the incident ray with the corresponding angle values.
(Given, )

Figure in the paper: Right-angled prism ABC with right angle at B, angle 45° at C, vertical side AB, horizontal base BC, hypotenuse AC. A horizontal ray enters face AB normally and strikes AC; in Fig. 1 it grazes along AC after refraction. In Fig. 2 the region on the AC side is filled with a liquid of refractive index 2/√3. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

Open one hint at a time and try again before the next.

Hint 1

A ray entering normally is not deviated; use the prism angles to find the angle of incidence on AC.

Hint 2

Grazing emergence means the angle of incidence equals the critical angle.

Hint 3

With the liquid present, find the new critical angle using the relative refractive index, then apply Snell's law.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

  1. (I) The ray enters face AB normally and goes undeviated. From the geometry of the prism (∠C = 45°), it meets face AC at an angle of incidence of 45°.

    ½ mark

  2. Since the ray grazes along AC, 45° is the critical angle:

    ½ mark

  3. (II)(a) Refractive index of glass relative to the liquid: , so , giving . The angle of incidence (45°) is less than C', so the ray neither grazes nor suffers total internal reflection; it is refracted into the liquid.

    1 mark

  4. Snell's law at AC:

    ½ mark

  5. (b) Ray diagram (described): the ray enters AB normally (0°), goes straight to AC and meets it at 45° to the normal. It then enters the liquid bent away from the normal, making 60° with the normal to AC.

    ½ mark

Answer: (I) ; (II) critical angle 54.6° > 45°, so the ray refracts into the liquid at

Where the marks are

  • Angle of incidence on AC is 45° (½ mark)
  • n = √2 from the critical-angle condition (½ mark)
  • Relative critical angle 54.6° compared with 45°: refraction occurs (1 mark)
  • Angle of refraction 60° and ray diagram (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Ray Optics and Optical Instruments, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2024-25: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.