# A phase difference of \pi/3 radians equivalent to a path difference of: a) six wavelengths b)...

## Question:

A phase difference of {eq}\pi/3 {/eq} radians equivalent to a path difference of:

a) six wavelengths

b) three wavelengths

c) one-third of a wavelength

d) one-sixth of a wavelength

## Path Difference:

The waves are characterized by their wavelength. When two waves interfere, they may give constructive or destructive interference depending on the path difference between them. A path length of one wavelength represents a phase of {eq}2\pi{/eq} radians.

Finding the path difference ({eq}\Delta x{/eq}) for a phase difference of {eq}\phi\ = \pi/3\ radians{/eq}

For a wave:

• {eq}2\pi\ radians {/eq} represents one wavelength i.e.{eq}\lambda{/eq}
• Therefore, the path difference corresponding to phase difference of {eq}\phi\ = \pi/3\ radians{/eq} is calculated as:
{eq}\Delta x\ = \dfrac{\lambda}{2\pi}\times \phi\\\Delta x\ = \dfrac{\lambda}{2\pi}\times \pi/3\\\Delta x\ = \dfrac{\lambda}{6}{/eq}

Correct option is (d) 