Question

The ratio of phase difference and path difference is:
A. $2\pi$
B. $\dfrac{{2\pi }}{\lambda }$
C. $\dfrac{\lambda }{{2\pi }}$
D. $\dfrac{\pi }{\lambda }$

Answer 1

To solve this question, we must have a basic concept about the path difference and phase difference. Phase difference is the difference in the phase angle of the two waves while the path difference is the difference in the path traversed by the two waves. We will see the relation between them and then proceed to solve the question accordingly.

Formula used:
The relation between the phase difference and path difference is given below.
$\Delta x = \dfrac{\lambda }{{2\pi }}\Delta \phi$
Where
$\Delta x$ is the path difference of the two waves
$\Delta \phi$ is the phase difference of the two waves
$\lambda$ is the wavelength of the two waves

Complete step-by-step answer:
From the relation above between the path difference and the phase difference, the ratio between them is given as
$\Rightarrow \Delta x = \dfrac{\lambda }{{2\pi }}\Delta \phi \\\ \Rightarrow \dfrac{{\Delta \phi }}{{\Delta x}} = \dfrac{\lambda }{{2\pi }} \\\$
Thus, the ratio between them is $\dfrac{\lambda }{{2\pi }}$
Hence, the correct option is B

Additional Information - A wave front is a surface with a constant phase of an optical wave over it. The wave front. The shape of a wavefront usually depends on the source's geometry, for example, could be the surface above which the wave has a maximum (for instance, the crest of a wave) or a minimum (the same wave) value. A source point has wave fronts which are spheres with the centers at the source point.

Note: The uses of path difference includes calculation of position of fringe width during Young double slit experiment while the phase difference is used when there is a constant phase relationship between the two waves i.e. the phase of the waves may vary but their difference is constant. Also, when two waves are in phase, then their peak will coincide with each other.