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?

Answer 1

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.