Question

A source emitting light of wavelengths 480 nm and 600 nm is used in a double-slit interference experiment. The separation between the slits is 0⋅25 mm and the interference is observed on a screen placed at 150 cm from the slits. Find the linear separation between the first maximum (next to the central maximum) corresponding to the two wavelengths.

Answer 1

Given:
Wavelengths of the source of light,
${\lambda }_1=480\times {10}^{-9}\mathrm{m}\mathrm{and}{\lambda }_2=600\times {10}^{-9}\mathrm{m}$
Separation between the slits, $d=0.25\mathrm{mm}=0.25\times {10}^{-3}\mathrm{m}$
Distance between screen and slit, $D=150\mathrm{cm}=1.5\mathrm{m}$
We know that the position of the first maximum is given by
$y=\frac{\lambda D}{d}$
So, the linear separation between the first maximum (next to the central maximum) corresponding to the two wavelengths = y₂ − y₁
$y_2-y_1=\frac{D\left(y_2-y_1\right)}{d}$

$$\begin{gathered} \Rightarrow y_2-y_1=\frac{1.5}{0.25\times {10}^{-3}}\left(600\times {10}^{-9}-480\times {10}^{-9}\right) \\ {y}_2-y_1=72\times {10}^{-5}\mathrm{m}=0.72\mathrm{mm} \end{gathered}$$