Question

If the distance between two slits is 1.5 µm and the distance to a screen is 1.5 m, find the angular spacing between the first-order bright fringes for light of 632 nm and 659 nm wavelength.

Answer 1

Angular position of first order bright fringe is given by

$dsin\theta = m\lambda$

where m = 1 for first order bright fringe

$sin\theta = \frac{m\lambda}{d}$

$sin\theta = \frac{m*\lambda}{d}$

here for first wavelength i.e. 632 nm

$sin\theta = \frac{1*632nm}{1.5\mu m}$

$sin\theta =0.42$

$\theta =sin^{-1}0.42 = 24.92^0$

Now for another wavelength i.e. 659 nm

$sin\theta = \frac{m\lambda}{d}$

$sin\theta = \frac{1*659nm}{1.5\mu m}$

$sin\theta = 0.44$

$\theta =sin^{-1} 0.44$

$\theta =26.1^0$

Now angular seperation between them is given by

$\Delta \theta =26.1^0 - 24.92^0 = 1.14^0$