Question

A point is situated at $6.5cm$ and $6.65cm$ from two coherent sources. Find the nature of illumination at the point. If the wavelength of light is \[{\text{5000}}\mathop {\text{A}}\limits^{\text{o}} \].

Answer 1

Hint: If their frequency and waveform are the same and their difference in phase is constant, wave sources are perfectly coherent.

Complete step-by-step answer:
Given
When two or more alternating quantities reach their maximum or zero values, Phase Difference is used to describe the difference in degrees or radians.
Consider ${x_1}$ and ${x_2}$ are path such that,
${x_1} = 6.5cm = 6.5 \times {10^{ - 2}}m,$
${x_2} = 6.65cm = 6.65 \times {10^{ - 2}}m,$
It is possible to describe wavelength as an image that reflects an audio signal or a recording. It illustrates the amplitude modifications over a certain amount of time. The signal amplitude is measured (vertically) on the y-axis, while time is measured (horizontally) on the x-axis.
${\lambda = 5000}\mathop {\text{A}}\limits^{\text{o}} = 5 \times {10^{ - 7}}m,$
To find nature of the illumination at the point,we use formula
$\Delta x = n\lambda $,
where $\Delta x$=path difference$(\Delta x = {x_2} - {x_1})$,\[\]
n$ = $nature of the illumination at that point,
$\lambda = $wavelength
Now, by using formula
${\text{n = }}\dfrac{{\Delta{\text{ x}}}}{\lambda{\text{}}}$${\text{ = }}\dfrac{{{{\text{x}}_{\text{2}}}{\text{ - }}{{\text{x}}_{\text{1}}}}}{\lambda{\text{}}}$
${\text{n = }}\dfrac{{6.65 \times {{10}^{ - 2}} - 6.5 \times {{10}^{ - 2}}}}{{5 \times {{10}^{ - 7}}}}$
$n = 3000$

Note: Frequency is the number of occurrences per unit of time of a repeating event. It is also referred to as temporal frequency, where the contrast between spatial frequency and angular frequency is emphasised. The frequency is measured in hertz (Hz) units, which is equal to one repeated event occurrence per second.