## 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* – *YP*when the point *P* is (i) At the bright band of 10^{th} order, (ii) At the dark band between third and fourth order maxima.

### Solution

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^{–5}cm and for 10^{th} order bright band, *m* = 10. The path difference for this band is

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

(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

#### SIMILAR QUESTIONS

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*h*= 6.63 × 10

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