Question

$FIGUREP33.36$shows the light intensity on a screen behind a double slit. The slit spacing is $0.20mm$and the wavelength of the light is $620nm$. What is the distance from the slits to the screen?

Short answer

The screen's length from the slits is$L=1.61\mathrm{m}.$

Step-by-step solution

Step: 1 Screen slit:

The fringe width reduced as the slit spacing improved, indicating reduced interference. The fringe width rose as the distance between the slits and the wall improved, because the light would have more area to diffract outwards and so interfere more.

Step: 2 Finding spacing fringes:

The distance between any two subsequent fringes in a double slit experiment is provided by the following relation.

$\mathrm{\Delta }y=\frac{\lambda L}{d}.$

The spacing between five peaks is comparable to role="math" localid="1649086556897" $\left(4∆y\right)$in $FIGUREP33.36$. As a result, the distance between any two consecutive fringes is

$$\begin{gathered} \mathrm{\Delta }y=\frac{2\mathrm{cm}}{4} \\ \mathrm{\Delta }y=0.5\mathrm{cm}. \end{gathered}$$

Step: 3 Finding slit screen distance:

Distance of screen slit by

$$\begin{gathered} L=\frac{d\mathrm{\Delta }y}{\lambda } \\ L=\frac{\left(0.2\times {10}^{-3}\mathrm{m}\right)\times 0.5\times {10}^{-2}\mathrm{m}}{620\times {10}^{-9}\mathrm{m}} \\ L=1.61\mathrm{m}. \end{gathered}$$