A plane light wave falls at an angle (not along the normal) from air on to a water surface. How many of the following remain the same after refraction?
Frequency, wavelength, speed, plane shape of the wavefront, angle between the wavefront and the surface, angle between a ray and the wavefront, phase difference between two points on the wavefront
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Four
On refraction into water the wave keeps its frequency but moves more slowly. So its wavelength falls and the wavefront turns towards the surface.
The quantities that remain the same:
Frequency — set by the source
Plane shape of the wavefront — the refracted wavefront is again a plane
Angle between a ray and the wavefront — rays stay perpendicular to the wavefront (\( 90^\circ \))
Phase difference between two points on the wavefront — zero, as a wavefront is a surface of constant phase
The quantities that change:
Wavelength — decreases in water
Speed — decreases in water
Angle between the wavefront and the surface — changes from \( i \) to the smaller angle \( r \)
Number of quantities that remain the same = 4
NCERT (2026-27):
Refraction of a plane wave – “The above equation implies that when a wave gets refracted into a denser medium (v1 > v2) the wavelength and the speed of propagation decrease but the frequency ν(= v/λ) remains the same.”
Refraction of a plane wave – “… Let CE represent a tangent plane drawn from the point C on to the sphere. Then, AE = v2τ and CE would represent the refracted wavefront. …”
Summary – “… The rays are then perpendicular to both the wavefronts and the time of travel is the same measured along any ray. …”
Huygens Principle – “… Such a locus of points, which oscillate in phase is called a wavefront; thus a wavefront is defined as a surface of constant phase. …”