a beam of light consisting of two wavelengths 800nm and 600 nm is used to obtain the interference pattern in youngs double slit expt on a screen placed 1.4m away.if two slits are separated by 0.28mm,calculate the least distance from the central bright maximum where the bright fringes of the two wavelenghts coinside..? plz help
for the 600nm wavelength, then nth fringe occurs at
n*600*10^-9m * 1400mm/.28mm = n*.003m
for the 800 nm, it's n*.004m
So, the first coincidence is at .012m
This is discussed in an identical problem at
http://www.physicsforums.com/showthread.php?t=364763
To calculate the least distance from the central bright maximum where the bright fringes of the two wavelengths coincide, we can use the equation for the position of the bright fringes in Young's double-slit experiment:
y = (m * λ * L) / d
where:
y is the distance from the central bright maximum,
m is the order of the fringe (m = 0 for the central maximum),
λ is the wavelength of light,
L is the distance from the double slits to the screen,
d is the separation between the slits.
In this case, we can calculate the distances separately for the two wavelengths and find the least distance where the two coincide.
For the 800 nm wavelength:
m = 0
λ = 800 nm = 8 × 10^-7 m
L = 1.4 m
d = 0.28 mm = 0.28 × 10^-3 m
Using the formula, we find the position of the central bright fringe for the 800 nm wavelength:
y1 = (0 * 8 × 10^-7 m * 1.4 m) / (0.28 × 10^-3 m)
y1 = 0
For the 600 nm wavelength:
m = 0
λ = 600 nm = 6 × 10^-7 m
L = 1.4 m
d = 0.28 mm = 0.28 × 10^-3 m
Using the formula, we find the position of the central bright fringe for the 600 nm wavelength:
y2 = (0 * 6 × 10^-7 m * 1.4 m) / (0.28 × 10^-3 m)
y2 = 0
From the calculations, the central bright fringes for both wavelengths coincide at y = 0, which means they coincide at the central maximum itself.
Therefore, the least distance from the central bright maximum where the bright fringes of the two wavelengths coincide is 0.
To calculate the least distance from the central bright maximum where the bright fringes of the two wavelengths coincide, we can use the equation for the bright fringe spacing in a Young's double slit experiment:
d * sinθ = m * λ
where:
- d is the separation between the two slits (0.28 mm),
- θ is the angle between the central maximum and the desired fringe,
- m is the order of the fringe (in this case, m = 0 since we are looking for the central maximum),
- λ is the wavelength of light.
To find the least distance where the bright fringes of the two wavelengths coincide, we need to determine the angles at which these fringes occur. We can then find the difference between the two angles to find the desired distance.
Let's start by finding the angles θ800nm and θ600nm for the two wavelengths using the equation above.
For λ = 800 nm (wavelength of the first beam):
d * sinθ800nm = m * λ800nm
0.28 mm * sinθ800nm = 0 * 800 nm
sinθ800nm = 0
θ800nm = 0 degrees
For λ = 600 nm (wavelength of the second beam):
d * sinθ600nm = m * λ600nm
0.28 mm * sinθ600nm = 0 * 600 nm
sinθ600nm = 0
θ600nm = 0 degrees
Both wavelengths have their bright fringes at θ = 0 degrees, which means that they coincide at the central maximum.
Hence, the least distance from the central bright maximum where the bright fringes of the two wavelengths coincide is equal to 0.