Question

Refractometry is an analytical method based on the difference between the speed of light as it travels through a substance (v) and its speed in a vacuum (c). In the procedure, light of known wavelength passes through a fixed thickness of the substance at a known temperature. The index of refraction equals c/v. Using yellow light (λ = 589 nm) at 20°C, for example, the index of refraction of water is 1.33 and that of diamond is 2.42. Calculate the speed of light in (a) water and (b) diamond.

Answer 1

Answer:

a). $2.25 \times 10^{8}$ m/s

b).  1.23 m/s                                

Explanation:

Given :

Index of refraction for water, $n_{w}$ = 1.33

Index of refraction of diamond, $n_{d}$ = 2.42

We know that,

Refractive index of any material is given by,

$n = \frac{c}{v}$

where c = sped of light in air

            v = speed of light in any medium

a). Speed of light in water

   $v = \frac{c}{n_{w}}$

   $v = \frac{3\times 10^{8}}{1.33}$

   $v = 2.25\times 10^{8}$ m/s

b). Speed of light in diamond

    $v =\frac{c}{n_{d}}$

   $v =\frac{3\times 10^{8}}{2.42}$

      = 1.23 m/s