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

a).
`2.25 * 10^(8)` m/s

b). 1.23 m/s

Step-by-step 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 = (c)/(v)`

where c = sped of light in air

v = speed of light in any medium

a). Speed of light in water

`v = (c)/(n_(w))`

`v = (3* 10^(8))/(1.33)`

`v = 2.25* 10^(8)` m/s

b). Speed of light in diamond

`v =(c)/(n_(d))`

`v =(3* 10^(8))/(2.42)`

= 1.23 m/s