19. In Young’s double slit experiment the separation d between the slits is 2 mm, the wavelength λ of the light used is 5896Å 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 ?

19. In Young’s double slit experiment the separation d between the slits is 2 mm, the wavelength λ of the light used is 5896Å 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) 1.8 mm

(b) 1.9 mm

(c) 1.7 mm

(d) 2.1 mm

Answer :  (b) 1.9 mm

\( \theta_{\text{width}} = \tfrac{\lambda}{d} \)

\( 0.20^{\circ} = \tfrac{5896 \, \text{Å}}{2 \, \text{mm}} \)

\( 0.21^{\circ} = \tfrac{5896 \, \text{Å}}{d_{2}} \)

\( \tfrac{0.20 \times 2}{0.21} = d_{2} \)

\( d_{2} = 1.9 \, \text{mm} \)