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Wave Optics

Question
CBSEENPH12039894

In young's double-slit experiment, the slits are 2 mm apart and are illuminated by photons of two wavelengths λ1 = 12000 A and λ2 =10000 A. At what minimum distance from the common central bright fringe on the screen 2 m from the slit will a bright fringe from one interference pattern coincide with a bright fringes from the other?

  • 8 mm

  • 6 mm

  • 4 mm

  • 3 mm

Solution

B.

6 mm

Given λ1 = 12000 Ao and λ2 = 10000 Ao
D = 2 cm and d=2 mm= 2x 10-3
We space have
straight lambda subscript 1 over straight lambda subscript 2 space equals space straight h subscript 1 over straight h subscript 2
space equals space 12000 over 10000 space equals space 6 over 5
as space straight x space equals space fraction numerator straight u subscript 1 straight lambda subscript 1 straight D over denominator straight d end fraction space equals space fraction numerator 5 space straight x space 12000 straight x space 10 to the power of negative 10 end exponent space straight x space 2 over denominator 2 space straight x space 10 to the power of negative 3 end exponent end fraction
equals space 5 straight x space 1.2 space straight x space 10 to the power of 4 space straight x space 10 to the power of negative 10 end exponent space straight x space 10 cubed space equals space 6 space mm