To demonstrate the phenomenon of interference, we require two sources which emit radiations of
(a) n

Q: Why can't two separate, identical light bulbs produce an interference pattern?

Even if two bulbs are identical and emit the same frequency, light is emitted by billions of independent atoms randomly. The phase difference between the two bulbs changes millions of times per second, causing the interference pattern to shift so fast that our eyes only see a uniform average intensity.

Q: Does a 'constant phase difference' mean the phase difference must be zero?

No. The phase difference can be any value—like $\pi/2$, $\pi$, or $45^\circ$—as long as it does not change as time passes. A constant phase difference ensures the maxima and minima stay in fixed positions.

Q: What happens if the amplitudes of the two coherent sources are different?

Interference will still occur! However, the dark fringes will not be perfectly dark (intensity won't be zero) because the waves cannot completely cancel each other out. The pattern will just have less contrast.

Q: Why is having the same frequency so important?

If the frequencies $f_1$ and $f_2$ are different, the phase difference between the waves is given by $\Delta \phi = 2\pi(f_1 - f_2)t$. Because time $t$ is always increasing, the phase difference will constantly change, destroying the stable pattern.

Q: How do we actually create coherent sources in a lab?

Since two independent sources are never perfectly coherent, we usually take a single light source and split it into two (like using two slits in Young's Double Slit Experiment). Because both new sources originate from the exact same parent wave, their phase relationship is perfectly locked.

Question

To demonstrate the phenomenon of interference, we require two sources which emit radiations of

Options:

(A) nearly the same frequency

(B) the same frequency

(C) different wavelength

(D) the same frequency and having a definite phase relationship

Sigma Percentile · Accepted Answer

### The Magic of Interference

Imagine dropping two pebbles into a perfectly calm pond. As the ripples spread out, they eventually meet and overlap. In some places, the crests of the waves add up to make a larger wave, and in other places, a crest and a trough cancel each other out, leaving the water perfectly flat. This beautiful, physical overlapping of waves is what we call **interference**.

However, seeing this pattern clearly on a screen using light waves is not as simple as turning on two flashlights. Light waves oscillate incredibly fast. If the pattern of bright and dark spots is constantly shifting millions of times per second, our eyes will just see a uniform blur of average light.

### The Need for Coherence

To observe a **sustained interference pattern**—where the bright fringes stay bright and the dark fringes stay dark—the mathematical conditions must be perfectly locked in place. The core requirement is that the phase difference, $\Delta \phi$, between the two interfering waves must remain absolutely constant over time.

Sources that can maintain this constant phase difference are called **coherent sources**.

### Breaking Down the Conditions

How do two sources achieve coherence?

First, they must have exactly the **same frequency** ($f_1 = f_2$). If one wave is oscillating even slightly faster than the other, the phase difference between them will continuously drift over time. Mathematically, if frequencies differ, the phase difference $\Delta \phi = 2\pi(f_1 - f_2)t$ becomes a function of time $t$, which destroys the stable pattern.

Second, having the same frequency is necessary but not sufficient. Two independent sodium lamps emit light of the exact same frequency, but the atoms inside emit light in random, spontaneous bursts. This means their phase relationship changes randomly every $10^{-8}$ seconds. Therefore, the sources must also have a **definite, locked phase relationship**.

### Evaluating the Options

When we look at the given choices:
- **(a) nearly the same frequency:** This will cause the phase difference to drift, washing out the pattern.
- **(b) the same frequency:** As discussed with the two sodium lamps, this alone doesn't guarantee a constant phase difference.
- **(c) different wavelength:** Different wavelengths mean different frequencies, which completely ruins coherence.
- **(d) the same frequency and having a definite phase relationship:** This perfectly encapsulates the definition of coherent sources.

Therefore, to demonstrate the phenomenon of interference, we strictly require sources that fit option (d).

Animated Solution for Physics - Optics: To demonstrate the phenomenon of interference, we require two sources which emit radiations of

Select Answer:

Visualized Solution

\text{The Phenomenon of Interference}

\text{Condition for Sustained Interference}

\text{Coherent Sources}

\text{Evaluating the Options}

\text{Final Conclusion}

The Sigma Insight: Interference and Young's Double-Slit Experiment

The Magic of Interference

The Need for Coherence

Breaking Down the Conditions

Evaluating the Options

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