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Question: In a double slit experiment, the distance between the slits is \(3mm\) and the slits are \(2m\) away...

In a double slit experiment, the distance between the slits is 3mm3mm and the slits are 2m2m away from the screen. Two interference patterns can be seen on the screen due to light with wavelength 480nm480nm, and the other due to light with wavelength 600nm600nm. What is the separation on the screen between the fifth bright fringes of the two interference patterns?

Explanation

Solution

Hint- Thomas Young carried out his double slit experiment to see the interference produced by the electrons. Those electrons are passing through the double slit. This double slit experiment is used to demonstrate the wave-particle duality nature of electrons and other particles. Both dark and bright fringes are shown on the screen.

Formula used:
y=nλDdy = \dfrac{{n\lambda D}}{d}
Where
yy=separation between the fringes
nn= order of the fringe
DD=distance between the slit and screen
dd= distance between the two slits

Complete step by step answer:
(i) Consider the beam of electrons is passing through slits. Those slits are separated by 3mm. After passing the slit, the electrons approach the screen which is 2m away from the slit. Those electrons made two interference patterns due to the light on wavelength 480nm and 600nm respectively.
(ii) The interferences occur on the both sides of the central fringe. The bright and dark fringes are occurring one by one on both sides. To find the distance between those fringes, we have to find the distance on both sides and have to find the difference between them. That is y2−y1{y_2} - {y_1}
(iii) Therefore, y1=nλ1Dd{y_1} = \dfrac{{n{\lambda _1}D}}{d}and {y_2} = \dfrac{{n{\lambda _2}D}}{d}$$$$$ {y_1} = \dfrac{{5 \times 480 \times {{10}^{ - 9}} \times 2}}{{3 \times {{10}^{ - 3}}}} \rightarrow {y_1} = 1.6 \times {10^{ - 3}}mAnd And{y_2} = \dfrac{{5 \times 600 \times {{10}^{ - 9}} \times 2}}{{3 \times {{10}^{ - 3}}}} \rightarrow {y_2} = 2 \times {10^{ - 3}}m(iv)Theseparationbetweenthefifthbrightorderfringesis, (iv)The separation between the fifth bright order fringes is, {y_2} - {y_1} = 2 \times {10^{ - 3}} - 1.6 \times {10^{ - 3}} \rightarrow 0.4 \times {10^{ - 3}}m(v)Thereforetheseparationbetweenthefifthorderbrightfringesis (v) Therefore the separation between the fifth order bright fringes is0.4 \times {10^{ - 3}}m$

Note: The electron beam from the source is passing through the slits and produces the pattern of interference fringes. The central bright fringe is followed by bright and dark fringes on its both sides. The electron beams make the interference pattern by interfering with themselves and this interference pattern explains the wave nature of the electrons.