In Young’s double slit experiment the separation d between the slits is 2 mm, the wavelength of λ the light used is 5896 mathring A and distance D between the screen and slits is 100 cm. It is found that the angular width of the fringes is 0.20°. To increase the fringe angular width to 0.21° (with same λ and D) the separation between the slits needs to be changed to

Question

In Young’s double slit experiment the separation d between the slits is 2 mm, the wavelength of λ the light used is 5896 mathring A and distance D between the screen and slits is 100 cm. It is found that the angular width of the fringes is 0.20°. To increase the fringe angular width to 0.21° (with same λ and D) the separation between the slits needs to be changed to (A) 1.7 mm (B) 1.8 mm (C) 2.1 mm (D) 1.9 mm

Tardigrade Admin · Accepted Answer

Angular width = (λ/d) 0.20° = (λ/2 mm) ...(i) 0.21° = (λ/d) ....(ii) Dividing we get, (0.20/0.21) = (d/ 2 mm ) ∴ d = 1.9 mm

1.7 mm

1.8 mm

2.1 mm

1.9 mm

Angular width =dλ​ 0.20∘=2mmλ​ ...(i) 0.21∘=dλ​ ....(ii) Dividing we get, 0.210.20​=2mmd​ ∴d=1.9mm

Angular width $= \frac{λ}{d}$
$0.2 0^{\circ} = \frac{λ}{2 mm}$ ...(i)
$0.2 1^{\circ} = \frac{λ}{d}$ ....(ii)
Dividing we get, $\frac{0.20}{0.21} = \frac{d}{2 mm}$
$∴ d = 1.9 mm$