In young's double slit experimental the separation d between the slits is 2 mm, the wavelength `lambda` of the light used is 5896Å and distance D between the screen and slitps 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 be changed to

Options

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

Answer

B

Explanation

In a YDSE, angular width of a fringe is given as
`theta=(lambda)/d)`
Where, `lambda` is the wavelength of the light source and d is the distance between the two slits.
`rArr theta propto 1/d` or `theta_(1)/theta_(2)=d_(2)/d_(1)`………….(i)
Here, `theta_(1)=0.20^(@)`, `theta_(2)=0.20^(@)`, `d_(1) = 2mm`
Substituting the given values in Eq. (i), we get
`0.20^(@)`/0.21^(@)` = d_(2)/(2mm) rArr d_(2) = 2 xx (0.20)/(0.21) = (0.40)/(0.21) = 1.90`mm