An Overview Of The Position Of Dark Fringes

The dark fringe formation is the resultant of the interferences which are destructive in nature. In the resultant amplitude, the interferences fringes are denoted as destructive and their intensity is equal to zero. At this point, a characteristic pattern of dark fringes and bright fringes is observed. This pattern is mainly resulting due to overlapping light waves’ “super-position”, which originates from two adjacent “slits”. Due to the light travelling at different positions have various distances from two adjacent slits to the “flat screen”, forming a double-slit interference pattern of alternating bright and dark bands. 

Dark fringe Position

The distance between 2 adjacent dark or bright colour fringes is mainly denoted as “fringe width”, calculated as the formula: “β = λD/d”. If the “resultant amplitude” is zero then the interference is determined as “destructive”. The position of dark or bright fringes in case of minimum intensity or the right fringes that generally formed as “P”. The difference of path is calculated as “Δz = (2n + 1) (λ/2) (n = 0, ±1, ±2, . . . .)”

That is, “x = (2n +1) λD/2d”. 

Hence, the distance of the “n” bright fringe from the “centre” is: “xn = (2n+1)λD/2d”.

Same as above, in the case of the distance of the “n-1” dark fringe from the “centre” is: “x (n-1)= (2(n-1) +1)λD/2d”. Hence, the width of Fringe can be calculated as: “β = xn  – x (n-1) = (2n + 1) λD/2d – (2(n -1) + 1)λD/2d = λD/d (n = 0, ±1, ±2, . . . .)”

The maximum intensity of bright fringes

In the pattern of interference, the fringes constant mainly relies on the “intensity ratio of sources”. When the ratio of the intensity of the sources is equal to “1”, then the intensity of the bright fringes is considered to be maximum and when the intensity of the source is equal to “0”, then the intensity of the dark fringe is minimum which is not good. The position of bright fringe colour that is much close to the central “achromatic fringe” in the pattern of interference with a white beam of light is medium. In the experiment of “Young Double-Slit”, the colour of the interference pattern that is obtained with “white light” is medium. 

Dark Fringe: discussion 

In Physics, Dark Fringe is often considered an “Interference fringe” which is bright in colour, mainly formed due to light beams that are present out-phase or in-phase with each other. Thomas Young became famous for establishing the phenomenon of “wavelike light nature”. The propagation of similar waves and light waves, when super-imposed add crests at their meeting point that is in the same phase. In dark fringes, when the troughs cancel the crests in their outer-phase, this specific phenomenon is known as destructive and constructive interference, respective to their positions. 

Single-Slit diffraction: Overview

In order to evaluate the consequences of the “wave nature” of light, it can be stated that diffraction in light occurs when they pass through a smaller slit. The wavelength which gets diffracted usually suffers destructive and constructive interferences with them, and then delivers the patterns of “single-slit diffraction”, which have alternating dark fringe and bright coloured fringes position. The formula that determines the dark fringe or bright coloured fringes’ location, can be stated as “w sin Θ = m λ”. In this formula, “w” is denoted as the width of “slit” and “m” is denoted as the dark fringe order. Θ is the angle created by slit centre line and the line that is connecting the dark fringe and slit and here λ is the “light wavelength” that is applied in this experiment.

Conclusion

The position of bright or dark fringes is often evaluated further by the experiment of “Young’s double-slit”. This experiment was first performed by Thomas Young, in the year 1801. His experiment includes 2 resulting beams of light which are directed to the flat screen, upon which interference fringes are created instead of forming 2 overlapping patches of light. These interference fringes are mainly identified as evenly “spaced alternating” dark and bright coloured bands. Interference fringes’ virtues that are formed help in the functioning of all “optical interferences”. To evaluate the condition of the dark fringes, it can be stated that when “monochromatic light” passes through 2 narrow slits usually illuminates a “distant screen”.