What are coherent sources, and why are they essential for interference?

Coherent sources are light sources that emit waves with the same frequency, same wavelength, and, most importantly, a constant phase difference between them over time. They are essential because for a stable and observable interference pattern to form, the positions of constructive and destructive interference must remain fixed. If the phase difference between the waves from two sources changes randomly, the bright and dark fringes would continuously shift, averaging out to a uniform illumination that our eyes cannot resolve into a distinct pattern. Only coherent sources ensure a sustained phase relationship.

How does the fringe width change if the Young's Double Slit Experiment (YDSE) apparatus is immersed in water?

If the entire YDSE apparatus is immersed in a medium like water, which has a refractive index ($\mu > 1$), the wavelength of light changes. The new wavelength ($\lambda'$) in the medium becomes $\lambda' = \frac{\lambda}{\mu}$, where $\lambda$ is the wavelength in air/vacuum. Since the fringe width ($\beta$) is directly proportional to the wavelength ($\beta = \frac{\lambda D}{d}$), the new fringe width ($\beta'$) will be $\beta' = \frac{\lambda' D}{d} = \frac{\lambda D}{\mu d} = \frac{\beta}{\mu}$. Therefore, the fringe width decreases, and the interference pattern shrinks.

What happens if white light is used instead of monochromatic light in YDSE?

When white light is used in YDSE, the central fringe remains white. This is because at the central position, the path difference for all wavelengths (colors) is zero, leading to constructive interference for every color. On either side of the central white fringe, colored fringes are observed. Since fringe width ($\beta = \frac{\lambda D}{d}$) depends on wavelength, each color produces its own interference pattern. Violet light (shortest wavelength) produces narrower fringes and appears closer to the central maximum, while red light (longest wavelength) produces wider fringes and appears farther away. After a few fringes, the patterns for different colors overlap significantly, causing the distinct fringes to disappear, and the screen appears uniformly illuminated.

Explain the role of path difference and phase difference in interference.

Path difference ($\Delta x$) is the difference in the distance traveled by two waves from their respective sources to a common point. Phase difference ($\Delta\phi$) is the difference in the phase angles of the two waves at that common point. These two are intrinsically linked by the relation $\Delta\phi = \frac{2\pi}{\lambda} \Delta x$. For constructive interference (bright fringes), the path difference must be an integral multiple of the wavelength ($\Delta x = n\lambda$), which corresponds to a phase difference of an even multiple of $\pi$ ($\Delta\phi = 2n\pi$). For destructive interference (dark fringes), the path difference must be an odd integral multiple of half the wavelength ($\Delta x = (n + \frac{1}{2})\lambda$), corresponding to a phase difference of an odd multiple of $\pi$ ($\Delta\phi = (2n+1)\pi$). These conditions dictate where light energy is redistributed.

How does introducing a thin transparent sheet in the path of one slit affect the interference pattern?

Introducing a thin transparent sheet of thickness 't' and refractive index '$\mu$' in the path of light from one slit introduces an additional path difference of $(\mu - 1)t$. This means the light from that slit effectively travels a longer optical path. As a result, the entire interference pattern shifts. The central bright fringe, which normally forms where the path difference is zero, now shifts to a new position where this additional path difference is compensated. The shift is given by $\Delta y = \frac{D}{d}(\mu - 1)t$, and it occurs towards the side of the slit where the sheet was placed. Importantly, the fringe width ($\beta$) remains unchanged because the relative path difference between consecutive fringes is still determined by the original wavelength and geometry.

Interference of Light

Physics

NEET UG

Version 1Updated 22 Mar 2026

Explore This Topic

Definition Deep Explanation Core Principles NEET Importance Problem Strategy Practice Problems MCQ Practice Quick Revision

Interference of light is a fundamental wave phenomenon where two or more coherent light waves superpose to form a resultant wave whose amplitude and intensity are either enhanced or diminished at various points in space. This redistribution of light energy results in a characteristic pattern of bright and dark fringes, known as an interference pattern. The phenomenon is a direct consequence of the…

Quick Summary

Interference of light is a wave phenomenon where two or more coherent light waves superpose, leading to a redistribution of light energy. This results in alternating bright (constructive interference) and dark (destructive interference) regions called interference fringes.

For observable interference, sources must be coherent (constant phase difference, same frequency/wavelength) and preferably monochromatic. Young's Double Slit Experiment (YDSE) is the classic demonstration.

In YDSE, the path difference between waves from two slits ( $S_1, S_2$ ) to a point P on a screen is approximately $\frac{yd}{D}$ , where y is the distance from the center, d is slit separation, and D is slit-screen distance.

Constructive interference occurs when path difference $\Delta x = n\lambda$ , leading to bright fringes at $y_n = \frac{n\lambda D}{d}$ . Destructive interference occurs when $\Delta x = (n + \frac{1}{2})\lambda$ , leading to dark fringes at $y_n' = (n + \frac{1}{2})\frac{\lambda D}{d}$ .

The fringe width, the distance between consecutive bright or dark fringes, is $\beta = \frac{\lambda D}{d}$ . The intensity at bright fringes is maximum ( $4I_0$ if $I_1=I_2=I_0$ ), and at dark fringes, it is minimum (0 if $I_1=I_2=I_0$ ).

Applications include thin film interference (soap bubbles, anti-reflection coatings).

Vyyuha

Your 6-Month Blueprint, Updated Nightly

AI analyses your progress every night. Wake up to a smarter plan. Every. Single.…

Key Concepts

Young's Double Slit Experiment (YDSE) Geometry and Path Difference

YDSE is the classical setup for observing interference. Light from a single source passes through two narrow…

Fringe Width and its Dependence on Parameters

The fringe width ( $\beta$ ) is the spatial separation between consecutive bright or dark fringes. It is given…

Effect of Thin Transparent Sheet on Fringe Pattern

When a thin transparent sheet of thickness 't' and refractive index ' $\mu$ ' is placed in the path of light…

Superposition Principle: — Resultant displacement is vector sum of individual displacements.

Coherent Sources: — Constant phase difference, same

\lambda

, same frequency.

Path Difference ($\Delta x$): — Difference in distances traveled.

Phase Difference ($\Delta\phi$): —

\Delta\phi = \frac{2\pi}{\lambda} \Delta x

Constructive Interference (Bright Fringes): —

\Delta x = n\lambda

\Delta\phi = 2n\pi

(

n=0,1,2...

I_{max} = 4I_0

Destructive Interference (Dark Fringes): —

\Delta x = (n + \frac{1}{2})\lambda

\Delta\phi = (2n+1)\pi

(

n=0,1,2...

I_{min} = 0

Fringe Width (YDSE): —

\beta = \frac{\lambda D}{d}

Position of Bright Fringes: —

y_n = \frac{n\lambda D}{d}

Position of Dark Fringes: —

y_n' = (n + \frac{1}{2})\frac{\lambda D}{d}

Effect of Medium (refractive index $\mu$): —

\lambda' = \frac{\lambda}{\mu}

\beta' = \frac{\beta}{\mu}

Shift due to Thin Sheet (thickness t, refractive index $\mu$): —

\Delta y = \frac{D}{d}(\mu - 1)t

. Shift is towards the side of the sheet.

For Wave Light, Double Slit Demonstrates Interference: Fringe Width is Lambda D over d.

Fringe Width ( $\beta$ ) = Lambda ( $\lambda$ ) * D (screen distance) / d (slit separation).