In Young's double slit experiment the separation d between the slits is `lambda` mm, the wavelength of the light used is 5896 Å 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 `lambda`. and D) the separation between the slits needs to change to .....

Options

A. `1.7` mm
B. `1.8` mm
C. `2.1` mm
D. `1.9` mm

Answer

D

Explanation

In Young.s experiment `d sin theta_(1)=(b) lambda`
If `theta` is very small, then `sin theta_(1) theta_(1)`
`:. d theta_(1)=lambda`
`:. theta_(1)=(lambda)/(d)`
`:.theta prop (lambda)/(d) [ :. lambda` and n are same]
`:. (theta_(2))/(theta_(1))=(d_(1))/(d_(2))`
`:. (0.21)/(0.20)=(2)/(d_(2)) rArr d_(2)`
`=(2xx0.21)/(0.20)`
`=1.9 mm`