In Young's double slit experiment the separation d between the sl… - Vidyadip

Question

In Young's double slit experiment the separation $d$ between the slits is $2\,\, mm,$ the wavelength $\lambda$ 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^o $ . To increase the fringe angular width to $0.21 ^o $ (with same $\lambda$ and $D$) the separation between the slits needs to be changed to ......$mm$

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Answer

Angular width $=\frac{\lambda}{d}$

${0.20^\circ } = \frac{\lambda }{{2\,{\text{mm}}}}$ .... $(i)$ and ${0.21^\circ } = \frac{\lambda }{d}$ ..... $(ii)$

Dividing we get, $\frac{{0.20}}{{0.21}} = \frac{d}{{2\,{\text{mm}}}}$

$\therefore $ $d=1.9 \mathrm{mm}$.

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