Profile
Settings
Refer your friends
Sign out
In this study, we looked at the displacement of the fringes in Young’s Double Slit Experiment. We used a laser to create a beam of light that passed through two slits and then onto a screen. We found that when the path length was changed, the displacement of the fringes also changed. This suggests that the displacement is caused by the difference in path length between the two slits.
What is the Displacement of fringes?
Displacement of fringes is the apparent movement of interference fringes when observed from a different position. This displacement is due to the difference in path length between the two waves. When viewed from the side, the displacement is equal to the difference in path length divided by the wavelength.
How can Displacement be seen?
The displacement can be seen in Young’s double-slit experiment, where two waves from the slits interfere to create fringes on a screen. If the screen is moved to the side, the fringes will appear to move as well. This displacement is due to the different path lengths of the two waves – one wave has traveled a longer distance than the other.
The displacement of fringes can also be seen in ripple tanks. When two waves meet, they create ripples on the surface of the water. If one wave is generated from a point closer to the observer, the ripples will appear to be displaced.
What causes Displacement?
Displacement is caused by the difference in path length between two waves. When two waves meet, they will interfere with each other. If one wave has traveled a longer distance than the other, it will have a different phase when they meet. This difference in phase will cause the displacement of fringes.
How can Displacement be measured?
The displacement of fringes can be measured by looking at the position of the fringes on a screen. If the screen is moved to the side, the fringes will appear to move as well. The displacement is equal to the difference in path length divided by the wavelength.
Solved problems on Displacement of fringes in Young’s Double Slit Experiment
Here are some problems with the displacement of fringes in Young’s double-slit experiment. The displacement is the distance between the central maximum and any other maxima or minima.
Problem
Two slits of width 0.100 mm are illuminated by a red laser (wavelength = 650 nm). If the separation between the slits is 0.250 mm, what is the displacement of the fourth-order bright fringe from the central maximum?
Given
Wavelength (λ) = 650 nm
Distance between slits (d) = 0.250 mm
Width of each slit (b) = 0.100 mm
Order of the bright fringe observed, n = fourth order
Displacement of the fourth-order bright fringe, x = ?
Solution
Displacement of the fourth-order bright fringe, x = (λ*d)/b
= (650 nm * 0.250 mm) / 0.100 mm
= 162.50 nm or 16.25 µm
(where µm represents micrometers)
Problem
In Young’s double-slit experiment, the slits are illuminated by red light (λ = 650 nm). If d = 0.300 mm and b = 0.050 mm, find the displacement of the sixth-order dark fringe from the central maximum.
Given
Wavelength (λ) = 650 nm
Distance between slits (d) = 0.300 mm
Width of each slit (b) = 0.050 mm
Order of the dark fringe observed, n = sixth order
displacement of the sixth-order dark fringe, x =?
Solution
displacement of the sixth-order dark fringe, x = -(λ*d)/b
= – (650 nm * 0.300 mm) / 0.050 mm
= -3900 nm or -390 µm
(where µm represents micrometers)
Conclusion
The displacement of the fringes in Young’s double-slit experiment is due to a difference in path length. When one slit is closed, the waves travel in a straight line and reach the screen at the same time. However, when both slits are open, the waves take different paths and arrive at the screen at different times. This causes a displacement of the fringes. The displacement can be calculated by measuring the distance between the two dotted lines on the screen. This is equal to the difference in path length between the two waves. So, if you want to know how much displacement there will be, just measure the path length difference and multiply it by the wavelength!
