significance of measuring velocity of light in different media

 Significance of measuring velocity of light in different media

To study various optical phenomena in different media, measuring velocity of light has great importance. 

i) The refractive index of medium is given by,

`\mu = \frac{c}{v}` .......................(1)

Where, c = velocity of light in vacuum

             v = velocity of light in medium

Relation (1) shows that measuring velocity in vacuum and in medium enables us to determine the refractive index of medium. We can estimate how denser is the medium by knowing velocity of light in the medium. 

For example, refractive index of a glass slab with respect to air is give as,

`a\mu_g = \frac{c}{v_g}`  .................(2) 

and refractive index of water with respect to air is given as,

`a\mu_w = \frac{c}{v_w}`  .................(3)

These relations (2) and (3) suggest that measuring velocity of light in different  media enables us to determine refractive indices for different media.

Divide (2) by (3) we get,

`\frac{a\mu_g}{a\mu_w} = \frac{\frac{c}{v_g}}{\frac{c}{v_w}}`

or, `\frac{a\mu_g}{a\mu_w} = \frac{c \times v_w}{v_g \times c}`

or, `\frac{a\mu_g}{a\mu_w} = \frac{v_w}{v_g}`

By the principle of reversibility, `\frac{1}{a\mu_w} = w\mu_a`, then

`w\mu_a \times a\mu_g = \frac{v_w}{v_g}`

or, `w\mu_g = \frac{v_w}{v_g}`

`\therefore` `w\mu_g = \frac{v_w}{v_g}` ..........(4)

 This is the expression that gives the refractive index of glass with respect to water. It is  valid when light travels from water to glass through the boundary between two media.

By the principle of reversibility,

`g\mu_w =  \frac{1}{w\mu_g} = \frac{v_g}{v_w}` ...........(5)

This expression gives the refractive index of water with respect to glass. It is valid when light passes from glass to water through glass-water boundary.

Note: 

Principle of reversibility: When the direction of light ray passing through vacuum to a medium is reversed, the ray follows the same path as it followed when passed through vacuum-medium boundary.  

ii) When electromagnetic wave travels through different media, the frequency  (`\nu`) of the wave remains constant. Thus, by measuring velocity(`v`) of light in different media, the wavelength(`\lamda`) of the wave in different media can be calculated using the relation, `\lamda = v/\nu`. The value of wavelength enables us to identify the type of the wave, that is, `\chi`-ray wave, Ultra-violet wave, radio-wave, Infra-red wave etc.