# 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

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?

#### 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
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#### APPEARS IN

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