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Two sources of light of wavelength 2.5 *10 -7 m and 3.5 *10 -7 m are used in Young’s double slit experiment simultaneously. Find out at which order of the two wavelength patterns the fringes coincide.

Two sources of light of wavelength 2.5 *10-7 m and 3.5 *10-7 m are used in Young’s double slit experiment simultaneously. Find out at which order of the two wavelength patterns the fringes coincide.

Grade:12th pass

1 Answers

Kapil Khare
80 Points
3 years ago
Let D be distance between slit and the screen.
Let d be distances between the two slits.
 
Wavelength of the first wavelength = 2.5 *10-7 m
Bright fringes for the first wavelength = n(2.5 *10-7 D/d)
 
Wavelength of the second wavelength =  3.5 *10-7 m
Bright finges for the second wavelength = m(3.5 *10-7 D/d)
 
For the two fringes coincides to coincides,
m(3.5 *10-7 D/d) = n(2.5 *10-7 D/d)
\implies    7m = 5n
\implies     m/n = 5/7
 
\implies So, the 5th bright fringe of second wavelength coincide with 7th bright fringe of first wavelength

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