In two separate set-ups of Young's double slit experiment using light of the same wavelength , fringes of equal width are observed .if ratio of slit separation in two is 2:3,find the ratio of the distance between source and screen placed in the two setups?
We know that the fringe width in Young's double slit experiment is given by
w = λD/d
where w is the fringe width, λ is the wavelength of light, D is the distance between the slits and the screen, and d is the slit separation.
Since the fringes in both setups have equal width, we can write
w1 = w2
Substituting the formula for w, we get
λD1/d1 = λD2/d2
Dividing both sides by λ, we get
D1/d1 = D2/d2
We are given that the ratio of slit separation in the two setups is
d1/d2 = 2/3
Substituting this in the above equation, we get
D1/(2/3) = D2/1
Simplifying, we get
D1/D2 = 2/3
Therefore, the ratio of the distance between source and screen placed in the two setups is 2:3.
In Young's double slit experiment, the fringe width (distance between adjacent fringes) can be given by the formula:
w = λD / d
Where:
w is the fringe width,
λ is the wavelength of light,
D is the distance between the source and the screen, and
d is the slit separation.
Given that the fringes of equal width are observed in two setups with the ratio of slit separations as 2:3, let's say the slit separation in the first setup is 2d and in the second setup is 3d.
Now, let's find the ratio of the distance between the source and the screen in the two setups.
The fringe width in both setups will be the same, so we have:
(w1 / w2) = (λD1 / (2d)) / (λD2 / (3d))
Simplifying this equation, we get:
w1 / w2 = (3D1) / (2D2)
Since the fringes of equal width are observed, w1 = w2. Therefore:
1 = (3D1) / (2D2)
Now, solving for the ratio of the distance between the source and the screen (D1 / D2):
D1 / D2 = 2 / 3
So, the ratio of the distance between the source and the screen in the two setups is 2:3.