ICSE Class 10 Answered
why does the speed increase or decrease in a medium i.e what are the factors that affect the speed of light in a medium and how?
Asked by asmithasrushti | 21 May, 2022, 18:56: PM
Maxwell has found out velocity v of electromagnetic radiation as
![begin mathsize 14px style v space equals space fraction numerator 1 over denominator square root of mu space cross times space epsilon end root end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/984c63111aed989b80ed0d3f248774e7.png)
where μ is magnetic permeability of medium and ε is electric permittivity of medium
For a transparent medium , μ = μr μo and ε = εr εo
where μr is relative permeabilty of medium, μo is permeability of free space ,
εr is relative permittivity or dielectric constant and εo is permittivity of free space.
Hence we can rewrite eqn.(1) as
![begin mathsize 14px style v space equals space fraction numerator 1 over denominator square root of mu subscript r space epsilon subscript r end root end fraction cross times 1 over square root of mu subscript o space cross times space epsilon end root subscript o end style](https://images.topperlearning.com/topper/tinymce/cache/ba951c45282086a7254d75497219ba64.png)
Let us consider velocity of light c in free space as
![begin mathsize 14px style c space equals space fraction numerator 1 over denominator square root of mu subscript o space cross times space epsilon subscript o end root end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/bbd5f2907cb45f9d54843b169f111120.png)
hence velocity of light in a medium can be written using eqn.(2) and eqn.(3) as
![begin mathsize 14px style v space equals space fraction numerator c over denominator square root of mu subscript r space epsilon subscript r end root end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/5ab5155542cb1a2f3dcb45ee577f5f9e.png)
Hence factors affecting speed of light in amedium are relative permeability and relative permittivity
Answered by Thiyagarajan K | 21 May, 2022, 22:58: PM
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