Two sources of monochromatic light are said to be coherent, if light waves produced by them have the same:
frequency and constant phase difference
Coherent Light Sources Conditions
When studying wave phenomena, especially interference, the concept of coherent sources is fundamental. Two sources of monochromatic light are said to be coherent if they emit light waves that maintain a constant phase relationship with each other over time. This stable relationship is absolutely essential for observing a clear and sustained interference pattern, like the bright and dark fringes seen in Young's Double-Slit Experiment.
For two monochromatic light sources to be truly coherent, they must fulfill two critical conditions:
- Frequency and Wavelength: The light waves generated by both sources must possess the exact same frequency. Since the speed of light (\(c\)) in a given medium is constant, and frequency (\(f\)) and wavelength (\(\lambda\)) are inherently linked by the universal wave equation, \(c = f\lambda\), having identical frequencies automatically ensures that their wavelengths are also identical. If the frequencies of the waves were different, their wavelengths would also differ, leading to a continuously changing relative phase, which would make a stable interference pattern impossible to observe.
- Constant Phase Difference: It is crucial that the phase difference between the light waves originating from the two sources remains constant throughout the observation period. This means that the relative position of the peaks and troughs of the two waves must not change over time. For example, if a peak from one wave aligns with a peak from the other at one instant, they should always maintain that specific phase relationship. If the phase difference were to vary randomly or rapidly, the constructive and destructive interference regions would constantly shift, resulting in a blurred or undetectable interference pattern.
In essence, for light waves to produce a steady and observable interference pattern, they must "march in step" with each other. This consistent "marching in step" is ensured by having both the same frequency and a constant phase difference between the waves.
Let's consider why the other options provided are not sufficient to define coherent sources:
- Frequency only: While having the same frequency is a necessary prerequisite for coherence, it is not by itself enough. Two waves can have the same frequency but an arbitrarily changing phase difference, which would not result in coherence or a stable interference pattern.
- Amplitude and same wavelength: Having the same wavelength implies that the sources have the same frequency. However, this option still omits the crucial condition of a constant phase difference. Amplitude primarily affects the brightness or intensity of the interference fringes, but it is not a defining characteristic for the coherence of the sources themselves.
- Amplitude only: This condition is entirely insufficient for defining coherence. Amplitude relates to the energy or intensity of the light wave and does not provide any information about the critical phase relationship or frequency that are fundamental to interference phenomena.
Therefore, for two monochromatic light sources to be considered coherent, they must satisfy both conditions: identical frequency and a constant phase difference between their emitted light waves.
Important Questions from Interference
- A single slit of width $a$ is illuminated by a monochromatic light of wavelength $\lambda_1 = 6000 \text{ Å}$. The angular width of the central maximum observed in the Fraunhofer diffraction pattern is $\theta_1$. When the slit width is increased by $20\%$ and the light source is replaced with another monochromatic light of wavelength $\lambda_2$, the angular width of the central maximum becomes $\frac{3}{5}$ of its initial value, $\theta_1$. Determine the wavelength $\lambda_2$.
A system of three polarizers $P_1$, $P_2$, $P_3$ is set up such that the pass axis of $P_3$ is crossed with respect to that of $P_1$.
The pass axis of $P_2$ is inclined at $15^\circ$ to the pass axis of $P_1$.
When a beam of unpolarized light of intensity $I_0$ is incident on $P_1$, the intensity of light transmitted by the three polarizers is $I$. The ratio $(I_0/I)$ equals (nearly):The interference pattern is obtained with two coherent light sources. If the ratio of their amplitudes is $n$, then in the interference pattern, the ratio $\frac{{{I_{max}} - {I_{min}}}}{{{I_{max}} + {I_{min}}}}$ will be
- Two identical coherent waves are superimposed at a point. If the maximum possible resultant intensity from their interference is $I_{max}$, and the resultant intensity at this point is $I_{max}/4$, then find the phase difference between the two waves at this point.
Which of the following sources gives best monochromatic light?
