Question

Find the ratio of intensity at the centre of a bright fringe

Answer 1

We have the formula for the intensity at a point in the interference pattern,

I=4I0cos2(ϕ/2)I=4I0cos2⁡(ϕ/2) … … … … (1)

I0I0 is the intensity due to either of the slit and ϕϕis the phase difference between the waves emitted from the two slits.

At the centre of the bright fringe the two waves are in phase (ϕ=0ϕ=0) and hence the intensity,

I1=4I0I1=4I0

Since the phase difference between the successive fringes is 2π2π hence the phase difference between the centre of a bright fringe and at a point one quarter of the distance between the two fringes away is 2π/4=π/22π/4=π/2. This then from equation (1) gives the intensity I2I2at that point,

I2=4I0cos2(π/4)=2I0I2=4I0cos2(π/4)=2I0

And, I1/I2=2