. In a Young double slit experiment the fringe separation produced by a wavelength of
5.00 x10-7m is 2mm at a distance of 2.5m. What would be the fringe separation produced by a wavelength of
400nm under the same setup.
To find the fringe separation produced by a wavelength of 400nm under the same setup in a Young double slit experiment, we can use the concept of the fringe separation formula:
Fringe separation (s) = (wavelength * distance to the screen) / distance between slits
Given values:
Wavelength of the first setup (λ1) = 5.00 x 10^-7 m
Fringe separation of the first setup (s1) = 2 mm = 2 x 10^-3 m
Distance to the screen of the first setup (D1) = 2.5 m
We can rearrange the formula to solve for the distance between slits:
Distance between slits (d) = (wavelength * distance to the screen) / fringe separation
Substituting the values into the formula:
d = (5.00 x 10^-7 m * 2.5 m) / (2 x 10^-3 m)
Calculating the result:
d = (1.25 x 10^-6 m) / (2 x 10^-3 m)
d = 6.25 x 10^-4 m
Now, we can use the calculated value of d and the wavelength of 400nm to find the fringe separation (s2) for the second setup:
s2 = (wavelength * distance to the screen) / distance between slits
s2 = (400 x 10^-9 m * 2.5 m) / (6.25 x 10^-4 m)
Calculating the result:
s2 = (1.0 x 10^-4 m) / (6.25 x 10^-4 m)
s2 ≈ 0.16 m
Therefore, the fringe separation produced by a wavelength of 400nm under the same setup is approximately 0.16 meters.