Question

In Young’s double slit experiment the separation $d$ between the slits is $2\, mm$, the wavelength of $\lambda$ 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 $0.20^{\circ}$. To increase the fringe angular width to $0.21^{\circ}$ (with same $\lambda$ 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

Answer 1

Answer: (D)

Angular width $= \frac{\lambda}{d}$
$ 0.20^{\circ} = \frac{\lambda}{2\,mm} \,\,\,\,\,$ ...(i)
$0.21^{\circ} = \frac{\lambda}{d} \,\,\,\,\,$ ....(ii)
Dividing we get, $\frac{0.20}{0.21} = \frac{d}{ 2\,mm } $
$\therefore d = 1.9\, mm $