Physics - Geometrical Optics Question with Solution | TestHub

The number of waves in a medium of thickness $t$ is given by $N=\frac{t}{{\lambda }_m}$, where ${\lambda }_m$ is the wavelength of light in that medium.

Since ${\lambda }_m=\frac{\lambda }{\mu }$, where $\lambda$ is the wavelength in vacuum and $\mu$ is the refractive index, we can write $N=\frac{t\mu }{\lambda }$.

Given that the number of waves in the glass slab is equal to the number of waves in the water column, we have:

$N_g=N_w$

$\frac{t_g{\mu }_g}{\lambda }=\frac{t_w{\mu }_w}{\lambda }$

$t_g{\mu }_g=t_w{\mu }_w$

Substituting the given values ($t_g=5$ cm, ${\mu }_g=1.56$, $t_w=6$ cm):

$5\times 1.56=6\times {\mu }_w$

$7.8=6{\mu }_w$

${\mu }_w=\frac{7.8}{6}=1.30$

Answer: 1.30