Case: Read the passage and answer the question.
The electromagnetic (EM) spectrum is the range of all types of EM radiation. Radiation is energy that travels and spreads out as it goes – the visible light that comes from a lamp in your house and the radio waves that come from a radio station are two types of electromagnetic radiation. The other types of EM radiation that make up the electromagnetic spectrum are microwaves, infrared light, ultraviolet rays, X-rays and gamma rays.
For the radiations named in the passage, a graph is drawn between the wavelength \(\lambda\) (on the y-axis) and the frequency \(\nu\) (on the x-axis) in vacuum. The graph is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → a rectangular hyperbola
All the radiations named in the passage travel in vacuum with the same speed \( c \). For each of them \( \nu\lambda=c \). So \( \lambda=c/\nu \), and the wavelength is inversely proportional to the frequency.
Option (1) a straight line through the origin with a positive slope — Incorrect. Such a line would need \( \lambda\propto\nu \). But a higher frequency gives a shorter wavelength.
Option (2) a straight line parallel to the frequency axis — Incorrect. This line would mean the same wavelength at every frequency. It is the speed \( c \) that stays the same, while the wavelength changes.
Option (3) a rectangular hyperbola — Correct. The product \( \nu\lambda \) has the same value \( c \) at every point of the graph. A graph with \( xy \) constant is a rectangular hyperbola.
Option (4) a straight line with a negative slope — Incorrect. On such a line, \( \lambda \) falls by equal amounts for equal rises in \( \nu \). With \( \lambda=c/\nu \), doubling \( \nu \) halves \( \lambda \), and the graph is a curve.
NCERT (2026-27):
Nature of electromagnetic waves – “This relation is often written in terms of frequency, ν (=ω/2π) and wavelength, λ (=2π/k) as”
\( \displaystyle 2\pi\nu=c\left(\frac{2\pi}{\lambda}\right) \quad \text{or} \quad \)\( \nu\lambda=c \)\( \qquad [8.9(b)] \)
Summary – “Light is an electromagnetic wave; c is, therefore, also the speed of light. Electromagnetic waves other than light also have the same velocity c in free space.”