In the Young’s double slit experiment with sodium light. The slits are 0.589 m a part. The angular separation of the third maximum from the central maximum will be (given λ = 589 mm)

(1) ${\mathrm{sin}}^{-1}\left(0.33×{10}^{8}\right)$

(2) ${\mathrm{sin}}^{-1}\left(0.33×{10}^{-6}\right)$

(3) ${\mathrm{sin}}^{-1}\left(3×{10}^{-8}\right)$

(4) ${\mathrm{sin}}^{-1}\left(3×{10}^{-6}\right)$

(4) Using relation, $d\mathrm{sin}\theta =n\lambda ⇒\mathrm{sin}\theta =\frac{n\lambda }{d}$

For n = 3, $\mathrm{sin}\theta =\frac{3\lambda }{d}=\frac{3×589×{10}^{-9}}{0.589}$

= 3 × 10–6 or $\theta ={\mathrm{sin}}^{-1}\left(3×{10}^{-6}\right)$

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