The electric and magnetic fields associated with an electromagnetic radiation in a medium are given as follows: E = 30 (2π × 10^18 rad s^-1 t + π × 10^10 m^-1 x)\ V m^-1 B = 10^-7 (2π × 10^18 rad s^-1 t + π × 10^10 m^-1 x)\ T I. What is the refractive index of the medium through which the wave is propagating? II. Find the frequency of the wave and identify the electromagnetic wave.

PhysicsCBSE Class 12 · Sample paper, session 2026-27 · 2 marks · Very short answer

CBSE Class 12 Physics sample paper 2026-27: question 17

From the official CBSE sample question paper for 2026-27, section B, question 17, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q17 · 2 marks · Very short answerElectromagnetic Waves

The electric and magnetic fields associated with an electromagnetic radiation in a medium are given as follows:

$E = 30 sin (2 π \times 1 0^{18} rad s^{- 1} t + π \times 1 0^{10} m^{- 1} x) V m^{- 1}$
$B = 1 0^{- 7} sin (2 π \times 1 0^{18} rad s^{- 1} t + π \times 1 0^{10} m^{- 1} x) T$

I. What is the refractive index of the medium through which the wave is propagating?
II. Find the frequency of the wave and identify the electromagnetic wave.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

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

Hint 1

The speed of a wave can be read from its equation as the ratio of the coefficient of t to the coefficient of x.

Hint 2

Refractive index is c divided by the speed in the medium.

Hint 3

Divide ω by 2π for frequency, then recall which part of the EM spectrum has ν around 10^18 Hz.

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.

Compare with $E = E_{0} sin (ω t + k x)$ : $ω = 2 π \times 1 0^{18}$ rad s $^{- 1}$ and $k = π \times 1 0^{10}$ m $^{- 1}$ . Speed in the medium: $v = \frac{ω}{k} = \frac{2 π \times 1 0 ^{18}}{π \times 1 0 ^{10}} = 2 \times 1 0^{8}$ m s $^{- 1}$ .
½ mark
Refractive index: $μ = \frac{c}{v} = \frac{3 \times 1 0 ^{8}}{2 \times 1 0 ^{8}} = 1.5$ .
½ mark
II. $ω = 2 π ν = 2 π \times 1 0^{18}$ , so $ν = 1 0^{18}$ Hz.
½ mark
A frequency of $1 0^{18}$ Hz (wavelength $\approx 1 0^{- 10}$ m) lies in the X-ray region.
½ mark

Answer: I. μ = 1.5; II. ν = 10^18 Hz, X-rays

Where the marks are

Finds wave speed $v = ω / k = 2 \times 1 0^{8}$ m/s (½ mark)
Gets $μ = c / v = 1.5$ (½ mark)
Finds $ν = 1 0^{18}$ Hz from $ω = 2 π ν$ (½ mark)
Identifies the wave as X-rays (½ mark)

Revise the chapter

Chapter: Electromagnetic Waves (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Electromagnetic Waves, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2026-27: every question, by section.

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CBSE Class 12 Physics sample paper 2026-27: question 17

Hints

Step-by-step solution

Revise the chapter

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