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Wave Optics question

2016 · Q118
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Wave Optics question

2016 · Q118

NEETPhysicsWave OpticsMCQ+4 / −1
In a diffraction pattern due to a single slit of width aaa, the first minimum is observed at an angle 30o when light of wavelength 5000 A∘\mathop A\limits^ \circA∘​ is incident on the slit. The first secondary maximum is observed at an angle of
  1. A
    sin−-−1(12)\left( {{1 \over 2}} \right)(21​)
  2. B
    sin⁡−1(34){\sin ^{ - 1}}\left( {{3 \over 4}} \right)sin−1(43​)
  3. C
    sin⁡−1(14){\sin ^{ - 1}}\left( {{1 \over 4}} \right)sin−1(41​)
  4. D
    sin⁡−1(23){\sin ^{ - 1}}\left( {{2 \over 3}} \right)sin−1(32​)
View written solutionFree

Correct answer: B

For the first minima, the path difference between extreme waves

sin θ\theta θ = λa{\lambda \over a}aλ​

⇒\Rightarrow⇒ 12{1 \over 2}21​ = λa{\lambda \over a}aλ​

⇒\Rightarrow⇒ aaa = 2λ\lambda λ

For first secondary maximum, the path difference between extreme waves

sin⁡θ′=3λ2a\sin \theta ' = {{3\lambda } \over {2a}}sinθ′=2a3λ​ = 32(12){3 \over 2}\left( {{1 \over 2}} \right)23​(21​)

⇒\Rightarrow⇒ θ′\theta 'θ′ = sin⁡−1(34){\sin ^{ - 1}}\left( {{3 \over 4}} \right)sin−1(43​)

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