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A Beam of Light Consisting of Two Wavelengths, 650 Nm and 520 Nm, is Used to Obtain Interference Fringes in a Young’S Double-slit Experiment. What is the Least Distance from the Central Maximum Where the Bright Fringes Due to Both the Wavelengths Coincide? - Physics

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A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes in a Young’s double-slit experiment.

What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?

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Solution

Wavelength of the light beam, lambda_1= 650 nm

Wavelength of another light beam, `lambda_2= 520 nm`

Distance of the slits from the screen = D

Distance between the two slits = d

Let the nth bright fringe due to wavelength `lambda_2` and (n − 1)th bright fringe due to wavelength lambda coincide on the screen. We can equate the conditions for bright fringes as:

`nlambda_2 = (n -1)lambda_1`

`520n = 650n - 650`

650 = 130 n

`:. n = 5`

Hence, the least distance from the central maximum can be obtained by the relation:

`x = nlambda_2 D/d`

`= 5xx582 D/d =  2600 D/d nm`

Concept: Interference of Light Waves and Young’S Experiment
  Is there an error in this question or solution?

APPEARS IN

NCERT Class 12 Physics Textbook
Chapter 10 Wave Optics
Q 6.2 | Page 383
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