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Strontium titanate is a rare… (Class 12 Physics 2023, Q35)

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PhysicsCBSE Class 12 · Board exam 2023, set 55/1/1 · 4 marks · Case-based

CBSE Class 12 Physics 2023: question 35

Set in the CBSE Class 12 board exam of 2023, paper 55/1/1, section E, question 35, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q35 · 4 marks · Case-basedCompetency-basedRay Optics and Optical Instruments

Strontium titanate is a rare oxide — a natural mineral found in Siberia. It is used as a substitute for diamond because its refractive index and critical angle are and , respectively, which are approximately equal to the refractive index and critical angle of diamond. It has all the properties of diamond. Even an expert jeweller is unable to differentiate between diamond and strontium titanate. A ray of light is incident normally on one face of an equilateral triangular prism ABC made of strontium titanate.

Answer the following questions based on the above :

  1. (a)

    Trace the path of the ray showing its passage through the prism.

    1 mark
  2. (b)

    Find the velocity of light through the prism.

    1 mark
  3. (c)

    Briefly explain two applications of total internal reflection.

    2 marks

  4. OR

    (c)

    Define total internal reflection of light. Give two conditions for it.

    2 marks

Figure in the paper: Equilateral triangular prism ABC with apex A at top (angle ), base BC at bottom. A ray is incident normally on face AB from the upper left. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 55/1/1.

Hints

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

Hint 1

A ray incident normally on a face does not bend. Find its angle of incidence on the next face using the 60° angles of the prism.

Hint 2

Compare that angle with the critical angle 24.5°. For the speed of light, use n = c/v.

Hint 3

Think of devices where light is trapped by repeated reflections inside a denser medium.

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. (a) The ray falls normally on face AB, so it enters the prism undeviated. Geometry of the equilateral prism gives an angle of incidence of on the next face it meets (BC). Since , the ray is totally internally reflected there. The reflected ray then strikes the third face AC normally and emerges into air without deviation.

    Diagram: the ray goes straight through AB, is totally reflected at BC at to the normal, and leaves perpendicular to AC.

    1 mark

  2. (b)

    1 mark

  3. (c) [first alternative] Application 1 – Optical fibres: Light enters one end of a thin glass or quartz fibre whose core is optically denser than its cladding. It strikes the core–cladding boundary at angles greater than the critical angle. It therefore undergoes repeated total internal reflections and travels along the fibre with very little loss. Fibres are used in telecommunication and endoscopy.

    1 mark

  4. Application 2 – Brilliance of diamond: Diamond has a very small critical angle (about ). Light entering a suitably cut diamond suffers multiple total internal reflections at its faces and comes out only through a few faces. This makes the diamond sparkle.

    (Mirage or totally reflecting prisms are also acceptable.)

    1 mark

  5. (c) [second alternative] Definition: When light travelling in an optically denser medium meets the boundary with a rarer medium at an angle of incidence greater than the critical angle, it is completely reflected back into the denser medium. This phenomenon is called total internal reflection.

  6. Conditions:
    1. Light must travel from an optically denser medium towards an optically rarer medium.
    2. The angle of incidence at the interface must be greater than the critical angle for that pair of media.

    (This alternative carries the same 2 marks as the first: definition 1 mark, conditions ½ + ½.)

Answer: (a) Enters undeviated, TIR at the second face (i = 60° > 24.5°), emerges normally from the third face; (b) v ≈ 1.24 × 10⁸ m/s; (c) optical fibres and brilliance of diamond / definition of TIR with its two conditions

Where the marks are

  • Traces the ray: undeviated entry, TIR at the second face since 60° > 24.5° (1 mark)
  • v = c/n = 1.24 × 10⁸ m/s (1 mark)
  • Two applications of TIR explained, e.g. optical fibre and diamond brilliance (1 + 1 marks)
  • OR: definition of TIR (1 mark) and two conditions (½ + ½ marks)

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 paper2023 board paper, set 55/1/1: 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.