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Q.Two statements are given – one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (a), (b),

(c) and
(d) as given below :
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is also false. Assertion (A) : The phase difference between any two points on a wavefront is zero. Reason (R) : All points on a wavefront are at the same distance from the source and thus oscillate in the same phase.
CBSECBSE Class XII Board 2023MCQ· 1mImportance★★★★★
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A wavefront is defined as the locus of points oscillating in phase; the reason correctly explains why — all points lie at equal optical path from the source. Both statements are true, and (R) explains (A).

The heart of this question lies in understanding what a wavefront actually is. When a wave propagates through space, we can identify surfaces where all points share the same phase of oscillation. These surfaces are wavefronts. The definition itself guarantees that any two points on the same wavefront oscillate in phase, which means the phase difference between them is zero.

Now let's examine each statement carefully.

Evaluating the Assertion

The assertion claims that the phase difference between any two points on a wavefront is zero. This is not just true — it is the defining characteristic of a wavefront.

When we draw a wavefront (spherical for a point source, planar for a distant source, etc.), we are tracing the set of all points that the wave disturbance reaches at the same instant, having traveled the same optical path length from the source. Since phase depends on the path traveled, equal path means equal phase.

Assertion (A) is true.

Evaluating the Reason

The reason states that all points on a wavefront are at the same distance from the source and thus oscillate in the same phase. This is the physical explanation for why the assertion holds.

For a point source emitting waves isotropically, a wavefront at time tt is a sphere of radius r=vtr = vt, where vv is the wave speed. Every point on this sphere is equidistant from the source. Since the phase of a wave at distance rr is given by

ϕ=ωt−kr+ϕ0\phi = \omega t - kr + \phi_0

where k=2πλk = \frac{2\pi}{\lambda} is the wave number, all points at the same rr have the same phase at any given time tt.

Even for more complex sources, the principle holds: a wavefront is constructed by connecting points that are reached by the wave after traveling equal optical path lengths (accounting for different media via refractive index). Equal optical path → equal phase.

Reason (R) is true. …

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