Fringes Of Unequal Intensities Are Obtained In Which Pattern

In the study of optics, interference patterns are some of the most fascinating and important phenomena. They reveal how light behaves as a wave and how two or more light waves interact with each other. One observation often discussed in physics is the formation of fringes of unequal intensities. This phenomenon occurs in specific interference patterns and helps distinguish one experimental setup from another. Understanding where fringes of unequal intensities are obtained requires looking at classic interference experiments, their principles, and the factors that influence fringe brightness.

Understanding Interference in Optics

Interference happens when two or more light waves overlap in space, producing regions of constructive and destructive interference. Where the crests of waves coincide, bright fringes are formed, and where crests overlap with troughs, dark fringes appear. These alternating bright and dark regions create a visible interference pattern.

Key Conditions for Interference

For interference fringes to be observed clearly, a few conditions must be satisfied

• The sources of light must be coherent, meaning they maintain a constant phase difference.
• The light should have the same frequency or wavelength for stable patterns.
• Overlapping of waves should occur under controlled geometry, such as through slits or reflection.

Where Unequal Intensity Fringes Appear

In interference experiments, the brightness of fringes depends on the amplitude of the waves combining. If the two interfering beams have equal intensity, the bright and dark fringes are sharply defined with maximum contrast. However, when the beams have unequal intensities, the resulting pattern displays fringes of unequal brightness. This is especially notable in certain interference setups.

Newton’s Rings

One experiment where fringes of unequal intensities are obtained is Newton’s rings. In this setup, a plano-convex lens is placed on a flat glass plate, creating a thin air film between the surfaces. When monochromatic light falls on the lens, interference occurs between the light reflected from the top and bottom surfaces of the air film. The result is a series of concentric circular fringes.

In Newton’s rings, the reflected system shows fringes of unequal intensities because one reflection occurs at the air-glass interface (with a phase change) and another at the glass-air interface (without phase change). The amplitudes of the reflected beams are not the same, which makes the bright and dark fringes uneven in sharpness and brightness.

Wedge-Shaped Film

Another pattern where unequal intensity fringes are observed is in a wedge-shaped film. This arrangement is formed when two glass plates are placed together at a small angle, creating a thin air wedge between them. When monochromatic light is incident, interference fringes appear in the form of parallel bands.

As with Newton’s rings, the reflected beams in the wedge-shaped film have different amplitudes due to differences in reflection at the two interfaces. This results in fringes of unequal intensities, with dark fringes appearing more distinct than bright ones.

Air Film in Reflected Light

In general, thin films observed in reflected light often produce fringes of unequal intensities. This is because one of the interfering beams usually suffers a phase shift of π (180 degrees) upon reflection, while the other does not. Moreover, reflection coefficients differ for each surface, leading to unequal amplitudes of the two beams.

Comparison With Young’s Double Slit Experiment

In contrast, the Young’s double slit experiment, another classic interference experiment, produces fringes of equal intensities provided the slits are identical and illuminated uniformly. Here, the two beams originate from the same coherent source and travel nearly equal distances, so their amplitudes remain equal. As a result, the bright fringes are of maximum brightness, and the dark fringes are perfectly dark, giving high contrast.

This difference highlights the importance of beam intensity in determining whether fringes are equal or unequal. While Young’s double slit shows equal intensity fringes, Newton’s rings and wedge-shaped films typically show unequal ones.

Mathematical Explanation of Unequal Intensities

The intensity of an interference pattern can be described mathematically. If two light waves of amplitudes A₁ and A₂ interfere, the resultant intensity I is given by

I = A₁² + A₂² + 2A₁A₂cosθ

Here, θ is the phase difference between the waves. When A₁ = A₂, the contrast is maximum, producing equal intensity fringes. But if A₁ ≠ A₂, the maxima and minima differ in brightness, leading to unequal intensity fringes. The visibility of fringes, defined as (Imax – Imin) / (Imax + Imin), decreases when amplitudes are unequal.

Practical Applications of Unequal Intensity Fringes

While fringes of unequal intensities may seem less perfect than equal ones, they still have important uses in physics and engineering. Such patterns are used in

• Measuring Wavelength of LightNewton’s rings experiment is commonly used to determine the wavelength of monochromatic light.
• Testing Lens SurfacesNewton’s rings can also reveal defects or irregularities on lens surfaces by examining the symmetry of fringes.
• Measuring Thin Film ThicknessWedge-shaped film fringes help calculate the thickness of very thin layers.
• Studying Refractive IndexBy analyzing fringe displacement in different media, the refractive index of liquids or solids can be determined.

Factors Affecting Fringe Intensity

Several factors influence whether fringes are equal or unequal in brightness

• Reflective PropertiesReflection at different interfaces may involve partial phase shifts and varying amplitude loss.
• Surface QualityImperfections on glass or lens surfaces can distort amplitudes, affecting fringe clarity.
• Coherence of LightIf the light source is not perfectly coherent, fringe visibility reduces and intensities become uneven.
• Medium Between SurfacesThe presence of air, liquid, or other media changes reflection conditions, altering fringe intensities.

Experimental Observation

In laboratory conditions, it is often easier to observe fringes of unequal intensities because achieving perfect equal amplitude beams is challenging. For example, in Newton’s rings, the central dark spot in reflected light is more distinct than the surrounding bright rings, illustrating the uneven intensity distribution. Similarly, wedge-shaped films show stronger dark bands compared to weaker bright bands.

Fringes of unequal intensities are obtained in interference patterns such as Newton’s rings, wedge-shaped films, and thin films observed in reflected light. These patterns differ from the idealized equal-intensity fringes of Young’s double slit experiment because the interfering beams do not have the same amplitude. The difference in intensity arises from variations in reflection coefficients, phase shifts, and optical paths. Despite being unequal, these fringes remain extremely useful in scientific experiments for measuring wavelength, testing optical components, and studying thin films. Recognizing where and why unequal intensity fringes appear enriches our understanding of wave optics and its practical applications in technology and research.