Question

Young's double slit experiment equations

Answer 1

Draw AM perpendicular to BP

The path difference δ = BP – AP

AP = MP

δ = BP – AP = BP – MP = BM

In right angled ? ABM, BM = d sin θ If θ is small,

sin θ = θ

The path difference δ = θ.d 

In right angled triangle COP, tan θ = OP/CO = x/D

For small values of θ, tan θ = θ

Thus, the path difference δ = xd/D
 

Bright Fringes

By the principle of interference, condition for constructive interference is the path difference = nλ

xd/D = nλ

Here, n = 0,1,2.....indicate the order of bright fringes

So, x = (D/d) nλ

This equation gives the distance of the nthbright fringe from the point O.

Answer 2

Answer:

The equation d sin θ = mλ (for m = 0, 1, −1, 2, −2, . . . ) describes constructive interference. For fixed values of d and λ, the larger m is, the larger sin θ is. However, the maximum value that sin θ can have is 1, for an angle of 90º.