Question

A glass slab of thickness 8 cm contains the same number of waves as 10 cm long path of water when both are traversed by the same monochromatic light. If the refractive index of water is 4/3, the refractive index of glass is

Answer 1

Frequency is constant wheras speed changes

4/3(10/8) = 40/24 =1.7

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Answer 2

Answer:

The refractive index of glass is 1.66.

Explanation:

Given that,

Thickness = 8 cm

Number of waves = 10 cm

Refractive index of water$n_{w} =\dfrac{4}{3}$

Let the wave length in glass =$\lambda_{g}$

The wavelength in water = $\lambda_{w}$

The number of wave in 8 cm glass = The number of wave in 10 cm water

$\dfrac{8}{\lambda_{g}}=\dfrac{10}{\lambda_{w}}$

We know,

$\lambda=\dfrac{\mu}{v}$

$\dfrac{\mu_{g}}{v}=\dfrac{8}{10}\dfrac{\mu_{w}}{v}$

Now, The refractive index is

$n_{g}=\dfrac{c}{\mu_{g}}$....(I)

$n_{w}=\dfrac{c}{\mu_{w}}$....(I)

The ratio of $n_{g}$ and $n_{w}$

$\dfrac{n_{g}}{n_{w}}=\dfrac{\mu_{w}}{\mu_{g}}$

$\dfrac{n_{g}}{n_{w}}=\dfrac{\mu_{w}}{\dfrac{8}{10}\mu_{w}}$

$\dfrac{n_{g}}{n_{w}}=\dfrac{10}{8}$

$n_{g}=\dfrac{10}{8}\times n_{w}$

$n_{g}=\dfrac{10}{8}\times\dfrac{4}{3}$

$n_{g}=\dfrac{5}{3}$

$n_{g}=1.66$

Hence, The refractive index of glass is 1.66.