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

                    

                                

SIMILAR QUESTIONS

Q1

 

(a) The wavelength of a given light is 0.00006 cm. Express this wavelength in micron and in angstrom. 

(b) What will be its wavelength in water, if the refractive index of water be 4/3.

Q2

The wavelength of a given light in vacuum is 6400 Ã…. Calculate its wavelength in water. Refractive index of water is 4/3.  

Q3

A light-ray of 6000 Ã… wavelength travelling in vacuum enters a medium of refractive index 1.5. Find the speed and the wavelength of the ray in the medium. 

Q4

The absolute refractive index of air is 1.0003 and the wavelength of yellow light in vacuum is 6000 Ã…. Find the thickness of air column which will have one more wavelength of the yellow light than in the same thickness of vacuum.

Q5

The number of waves in a 4-cm thick strip of glass is the same as in 5-cm water, when the same monochromatic light travels in them. If the refractive index of water be 4/3, what will be of glass?

Q6

What is the content of energy in X-ray photon of wavelength 10 Ã…? Given J-s,  

Q7

Calculate de-Broglie wavelength for an electron and a proton moving with the same speed of 105 m/s. (me = 9.1×10 –31 kg, mp = 1.67 × 10 –27 kg and h = 6.63 × 10 –34 Js).

Q8

The ratio of intensities of two waves is 25:16. What is the ratio of amplitudes? If these two waves produce interference, then find the ratio of maximum and minimum intensities.

Q9

Two waves of same frequency have amplitude in the ratio 2:1. Find the ratio of the maximum and the minimum amplitudes and intensities in the region of interference. 

Q10

In Young’s experiment on interference of light a fringe of width 0.04 cm is obtained on a screen placed at a distance of 50 cm from the slits when the wavelength of the light used is 5000 Ã…. If the distance of the screen from the slits remains unchanged, what will be the width of the fringe if light of wavelength 4000 Ã… is used?