Question

$FIGUREP33.36$shows the light intensity on a screen behind a double slit. The slit spacing is $0.20mm$and the screen is $2.0m$behind the slits. What is the wavelength (in $nm$) of the light?

Short answer

The light's wavelength is$\lambda =500nm.$

Step-by-step solution

Step: 1 wavelength light:

The wavelength of visible light is $400nm$to $700nm$, and this is where we understand about the widths of multiple colors in the visible spectrum of light.

Step: 2 Finding the width:

As per the diagram,since the width of four fringes is $20cm$, the width of one fringe will be

$$\begin{gathered} w=\frac{0.02}{4} \\ w=\underset{}{5\times {10}^{-3}\mathrm{m}}. \end{gathered}$$

We understand that the fringe thickness in the double-slit experiment is calculated as

$w=\frac{\lambda L}{d}.$

Step: 3 Obtaining the wavelength value:

The wavelength by

$\lambda =\frac{wd}{L}$

$\lambda =\frac{5\times {10}^{-3}\times 2\times {10}^{-4}}{2}$

$\lambda =5\times {10}^{-7}\mathrm{m}$

localid="1649147686306" $\lambda =500\mathrm{nm}.$