Question

In Young’s double slit experiment the separation 𝑑 between the slits is $2mm$, the wavelength $\lambda$ of the light used is $5896A^{\circ }$ and distance $D$ between the screen and slits is $100cm$. 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 in 𝑚𝑚 between the slits needs to be changed to

Answer 1

We know that: $\theta =\frac{\lambda }{d}$

Given:

$D=100cm=1m$

$d=2mm,\lambda =5896\stackrel{\circ }{A}$

for a given wavelength

$\frac{{\theta }_1}{{\theta }_2}=\frac{d_2}{d_1}\Rightarrow \frac{{0.20}^{\circ }}{{0.21}^{\circ }}=\frac{d_2}{2mm}$

$\Rightarrow 0.20\times 2=0.21\times d_2$

$\Rightarrow d_2=1.9mm$

The separation in $mm$ between the slits to be changed to $1.9mm$