Question

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The intensity of light originating from first slit is doubled the intensity from the second slit. What is ratio of the amplitudes of the two interfering waves?

Answer 1

The amplitude of the resulting wave is given by



∴ I = KA2

= K a12 + K a22 + 2 Ka1a2 cosφ

I = I1 + I2 + 2 √ I1 √ I2 cosφ

Where I1 and I2 are the intensities of the interfering waves.

If the amplitude of the interfering waves are equal

i.e. a1 = a2 = a (let) then,

from above we obtain

Imax = K(4a2) and

From above) we obtain

Imin = 0

The intensity vs phase difference (φ) curve of the resulting wave is shown in figure below:



Illustration :  The intensity of the light coming from one of the slits in a Young’s double slit experiment is double the intensity from the other slit. Find the ratio of the maximum intensity to the minimum intensity in the interference fringe pattern observed.

Solution: The intensity of the light originating from the first slit is double the intensity from the second slit. The amplitudes of the two interfering waves are in the ratio √2 : 1 , say √2 A and A .

At the point of constructive interference, the resultant amplitude becomes (√2 + 1) A. At the points of destructive interference , this amplitude is (√2 – 1)A.

The ratio of the resultant intensities at the maxima to that at the minima is

(√2 + 1)A2÷(√2 − 1)A2 =34