The ratio of the intensity at the centre of a bright fringe to the intensity at a point distant one fourth of the distance between two successive bright fringes will be?
Please answer ASAP. I have my IPU CET on 8th May.
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have the formula for the intensity at a point in the interference pattern,
I=4I0cos2(ϕ/2) … … … … (1)
I0 is the intensity due to either of the slit and ϕ is 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=0) and hence the intensity,
I1=4I0
Since the phase difference between the successive fringes is 2π 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/2. This then from equation (1) gives the intensity I2 at that point,
I2=4I0cos2(π/4)=2I0
And, I1/I2=2
I=4I0cos2(ϕ/2) … … … … (1)
I0 is the intensity due to either of the slit and ϕ is 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=0) and hence the intensity,
I1=4I0
Since the phase difference between the successive fringes is 2π 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/2. This then from equation (1) gives the intensity I2 at that point,
I2=4I0cos2(π/4)=2I0
And, I1/I2=2
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