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Wave Optics question

2013 · Q134
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Wave Optics question

2013 · Q134

NEETPhysicsWave OpticsMCQ+4 / −1
In Young's double slit experiment, the slits are 2 mm apart and are illuminated by photons of two wavelengths λ1{\lambda _1}λ1​ = 12000 A∘\mathop A\limits^ \circA∘​ and λ2{\lambda _2}λ2​ = 10000 A∘\mathop A\limits^ \circA∘​. 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 fringe from the other ?
  1. A
    4 mm
  2. B
    3 m
  3. C
    8 mm
  4. D
    6 mm
View written solutionFree

Correct answer: D

From the question, n1λ\lambda λ1 = n2λ\lambda λ2

So, n1n2=λ2λ1{{{n_1}} \over {{n_2}}} = {{{\lambda _2}} \over {{\lambda _1}}}n2​n1​​=λ1​λ2​​ = 1000012000=56{{10000} \over {12000}} = {5 \over 6}1200010000​=65​

Hence, minima n1 and n2 are 5 and 6.

Xmin = n1λ1Dd=5(12000×10−10)22×10−3{{{n_1}{\lambda _1}D} \over d} = {{5\left( {12000 \times {{10}^{ - 10}}} \right)2} \over {2 \times {{10}^{ - 3}}}}dn1​λ1​D​=2×10−35(12000×10−10)2​

= 6 × 10–3 m = 6 mm

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