Question

When light of wavelength $5000\mathring{A}$ in vacuum travels through same thickness in glass and water, the difference in the number of waves is $400$. Find the thickness (Refractive index of glass and water are $\frac{3}{2}$ and $\frac{4}{3}$ respectively)

Answer 1

Difference in no of waves=$\frac{l}{\lambda }\left({\mu }_g-{\mu }_w\right)-eq1$

where ${\mu }_g$ is reflective index of glass ${\mu }_w$is refractive index of water

${\mu }_s=\frac{3}{2},{\mu }_w=\frac{4}{3},\lambda =5000A$

putting these values in equation 1, we get

$\begin{array}{c}400=\frac{1}{5000\times {10}^{-10}}\left(\frac{3}{2}-\frac{4}{3}\right)\\ =\frac{1}{5\times {10}^{-7}}\times \frac{1}{6}\end{array}$

the thickness is:

$\begin{array}{c}l=400\times 5\times 6\times {10}^7\\ 1.2mm\end{array}$