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(A) The number of waves $N$ in a medium of thickness $t$ is given by $N = \frac{t}{\lambda_m}$, where $\lambda_m = \frac{\lambda_0}{\mu}$ is the wavel

Vedclass · Accepted Answer

$\frac{4}{3}$

Vedclass · Answer

(A) The number of waves $N$ in a medium of thickness $t$ is given by $N = \frac{t}{\lambda_m}$, where $\lambda_m = \frac{\lambda_0}{\mu}$ is the wavelength in the medium and $\lambda_0$ is the wavelength in vacuum.Thus, $N = \frac{t \cdot \mu}{\lambda_0}$.Given that the number of waves in the glass slab $(t_g = 4 \,cm, \mu_g = 5/3)$ is equal to the number of waves in the water column $(t_w = 5 \,cm, \mu_w = ?)$, we have:$\frac{t_g \cdot \mu_g}{\lambda_0} = \frac{t_w \cdot \mu_w}{\lambda_0}$$t_g \cdot \mu_g = t_w \cdot \mu_w$Substituting the given values:$4 	imes \frac{5}{3} = 5 	imes \mu_w$$\frac{20}{3} = 5 	imes \mu_w$$\mu_w = \frac{20}{3 	imes 5} = \frac{4}{3}$.

$A$ monochromatic ray of light travels through a glass slab and a water column. The number of waves in a glass slab of thickness $4 \,cm$ is the same as in a water column of height $5 \,cm$. If the refractive index of glass is $\frac{5}{3}$, then the refractive index of water is:

Similar Questions

$A$ ray of light is incident on one face of a transparent slab of thickness $15 \, cm$. The angle of incidence is $60^{\circ}$. If the lateral displacement of the ray on emerging from the parallel plane is $5\sqrt{3} \, cm$,the refractive index of the material of the slab is:

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$A$ layer of oil $3\,cm$ thick is floating on a layer of coloured water $5\,cm$ thick. The refractive index of coloured water is $5/3$ and the apparent depth of the two liquids appears to be $36/7\,cm$. Find the refractive index of oil.

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