Question
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?
Answers
Bot
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.
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.