Question

The figure(Figure 1) shows the light intensity on a screen behind a double slit. The slit spacing is 0.26mm and the screen is 2.1m behind the slits.

1- What is the wavelength (in nm) of the light?

Answer 1

From the figure, distance between four maxima \(Y=2.0 \mathrm{~cm}\)

Distance between successive bright fringes \(\Delta y=\mathrm{Y} / 4=0.5 \mathrm{~cm}=0.005 \mathrm{~m}\)

We know \(\Delta y=\frac{\lambda D}{d} \ldots \ldots \ldots \ldots \ldots(1)\)

\(d=0.26 \mathrm{~mm}=0.26 \times 10^{-3} \mathrm{~m}\)

\(\mathrm{D}=2.1 \mathrm{~m}\)

From equation (1)

\(\lambda=\frac{\Delta y d}{D}\)

\(\lambda=\frac{0.005 \times 0.26 \times 10^{-3}}{2.1}=619.04 \mathrm{nm}\)