Answer :
Refractive index of a medium is defined as the ratio of speed of light in vacuum to speed of light in the medium.
given [tex]v_g=2 \times 10^8\ m/s[/tex]
Let velocity in vacuum = v
refractive index of glass is 3/2.
(you have given wrong information.)
[tex]\eta_g = \frac{v}{v_g} \\ \\ \frac{3}{2}= \frac{v}{2 \times 10^8} \\ \\v= \frac{ 3 \times 2 \times 10^8}{2}= 3 \times 10^8\ m/s[/tex]
So speed of light in vacuum is [tex]3 \times 10^8\ m/s[/tex].
[tex]\eta_w= \frac{v}{v_w}\\ \\ \frac{4}{3}= \frac{3 \times 10^8}{v_w} \\ \\ v_w= \frac{3 \times 3 \times 10^8}{4} =2.25 \times 10^8\ m/s[/tex]
So speed of light in water is [tex]2.25 \times 10^8\ m/s[/tex]
given [tex]v_g=2 \times 10^8\ m/s[/tex]
Let velocity in vacuum = v
refractive index of glass is 3/2.
(you have given wrong information.)
[tex]\eta_g = \frac{v}{v_g} \\ \\ \frac{3}{2}= \frac{v}{2 \times 10^8} \\ \\v= \frac{ 3 \times 2 \times 10^8}{2}= 3 \times 10^8\ m/s[/tex]
So speed of light in vacuum is [tex]3 \times 10^8\ m/s[/tex].
[tex]\eta_w= \frac{v}{v_w}\\ \\ \frac{4}{3}= \frac{3 \times 10^8}{v_w} \\ \\ v_w= \frac{3 \times 3 \times 10^8}{4} =2.25 \times 10^8\ m/s[/tex]
So speed of light in water is [tex]2.25 \times 10^8\ m/s[/tex]
Answer:
Explanation:
Solution :-
Refractive index of a medium = Speed of light in air/Speed of light in medium
3/2 = Speed of light in air/2 × 10⁸ m/s
Speed of light in air = 3 × 10⁸ m/s
1. In Vacuum -
Speed of the light in vacuum = 2 × 10⁸ m/s/3/2
Speed of the light in vacuum = 3 × 10⁸ m/s
Hence, the speed of light in vacuum is 3 × 10⁸ m/s.
2. In Water -
Speed of the light in water = 3 × 10⁸ m/s/4/3
Speed of the light in water = 2.25 × 10⁸ m/s
Hence, the speed of light in water is 2.25 × 10⁸ m/s.