What is the speed of light in the medium whose refractive index is 3/2? Given speed of light is 3×10^8 m/s
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What is the speed of light in the medium whose refractive index is 3/2? Given speed of light is 3×10^8 m/s
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Given :-
◉ Speed of light, c = 3 × 10^8 m/s
◉ Refractive index of medium = 3/2
To Find :-
◉ Speed of light in the given medium
Solution :-
We know,
Refractive Index in terms of Speed of Light
⇒ Speed of Light in Air / Speed of Light in medium
Given, Refractive Index = 3/2
Now,
⇒ 3/2 = 3 × 10^8 / v
⇒ v = 2 × 10^8 m/s
Hence, Speed of Light in the given medium is 2 × 10^8 m/s
More Information :-
◉ Refractive Index of a medium m is the ratio of speed of light in air and the speed of light in the medium m.
◉ Refractive Index is also equal to ratio of sine of the angle of incidence and sine of the angle of refraction. which is also known as Snell's Law.
Given ,
Refractive index of medium = 3/2
Speed of light = 3 × (10)^8 m/s
We know that ,
[tex] \boxed{ \sf{Refractive \: index \: of \: medium \: (n) = \frac{speed \: of \: light \: in \: vaccum }{speed \: of \: light \: in \: medium } }}[/tex]
Thus ,
[tex]\sf \mapsto \frac{3}{2} = \frac{3 \times {(10)}^{8} }{speed \: of \: light \: in \: medium} \\ \\ \sf \mapsto speed \: of \: light \: in \: medium = 2 \times {(10)}^{ 8} \: m{s}^{ - 1} [/tex]
[tex] \sf \therefore \underline{The \: speed \: of \: light \: in \: medium \: is \: 2 \times {(10)}^{ 8} \: m{s}^{ - 1} }[/tex]