Question

In Lloyd's mirror experiment (Fig.) a light wave emitted directly be the source S (narrow slit) interferes with the wave reflected form a mirror M. As s result, an interference fringe pattern is formed on the screen Sc. the source and the mirror are separated by a distance l=100 cm. At a certain position of the source, the fringe width on the screen was equal to Δx=0.25 mm, and after source was moved away from the mirror plane by Δh=0.60mm, the fringe width decreased η=1.5 times. Find the wavelength of light.

Answer 1

From the general formula

$\Delta x=\frac{l\lambda }{d}$

we find that

$\frac{\Delta x}{\eta }=\frac{l\lambda }{d+2\Delta h}$

since $d$ increases to $+2\Delta h$ when the source is moved away from the plane mirror by $\Delta h$.

Thus

$\begin{array}{c}\eta d=d+2\Delta h\end{array}$

or $d=2\Delta h/(\eta -1)$

Finally

$\lambda =\frac{2\Delta h\Delta x}{(\eta -1)l}=0.6Microm$