Two Coherent Sources X and Y of Light Of Wavelength λ = 6.2 × 10 –5 cm, Produce Interference. If Both The Sources Are In The Same Phase And P is An Arbitrary Observation Point, Then Calculate XP – YPwhen The Point P is (i) At The Bright Band Of 10th order, (ii) At The Dark Band Between Third And Fourth Order Maxima.

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Question

 

Two coherent sources X and Y of light of wavelength

λ = 6.2 × 10 –5 cm, produce interference. If both the sources are in the same phase and P is an arbitrary observation point, then calculate XP – YPwhen the point P is (i) At the bright band of 10th order, (ii) At the dark band between third and fourth order maxima.

Solution

Correct option is

 

The intensity of light at a light at a point will be maximum or minimum when the path difference (XP – YP) is zero or an integral multiple of λ or an odd multiple of λ/2 respectively.

(i)                For maximum intensity (bright band), we have

Path difference (XP – YP) = m λ, where m = 0, 1, 2, 3,……..

Here λ = 6.2 × 10–5cm and for 10th order bright band, m = 10. The path difference for this band is

          (XP – YP) = 10 × (6.2 × 10–5) = 6.2 × 10–4cm.

(ii)             For the dark band, we have

There will be the fourth dark band between the third and the fourth order maximum (bright bands). The path difference for the fourth dark band (m= 4) is

                    

                                

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