Right answer: [tex]1.5({10}^{8})m/s[/tex]
The Absolute Refractive index [tex]n[/tex] is the quotient of the speed of light in vacuum [tex]c[/tex] and the speed of light in the medium whose index is calculated [tex]v[/tex], as shown in the expression below:
[tex]n=\frac{c}{v}[/tex] (1)
This is a dimensionless value.
If we know that:
[tex]c=3({10}^{8})m/s[/tex]
[tex]n_{1}=1[/tex] is the refractive index in vacuum
[tex]n_{2}=2[/tex] is the refractive index in the liquid
We can use equation (1), with the values of [tex]n_{2}[/tex] and [tex]c[/tex] to calculate [tex]v_{liquid}[/tex], which is the velocity of light in this medium:
[tex]n_{2}=\frac{c}{v_{liquid}}[/tex] (2)
[tex]v_{liquid}=\frac{c}{n_{2}}[/tex] (3)
[tex]v_{liquid}=\frac{3({10}^{8})m/s}{2}[/tex] (4)
Finally:
[tex]v_{liquid}=1.5({10}^{8})m/s[/tex]>>>>This is the speed of light in the liquid.
Therefore the correct option is c.
The speed of the light in the liquid whose refractive index is equal to 2.0 is 1.5×10⁸ m/s.
Speed of light is the rate of speed though the light travels. To find the speed of light in any medium, the following formula is used.
[tex]v=\dfrac{c}{n}[/tex]
Here, (n) is the index of reaction and (c) is the speed of light in the vacuum. The speed of light in the vacuum is almost equal to the 3.0×10⁸ m/s.
It is given that the Light having a speed in vacuum of 3.0×10⁸ m/s enters a liquid of refractive index 2.0. In this liquid. To find its speed, plug in the values in the above formula.
[tex]v=\dfrac{3\times10^{8}}{2}\\v=1.5\times10^8\rm\; m/s[/tex]
Hence, the speed of the light in the liquid whose refractive index is equal to 2.0 is 1.5×10⁸ m/s.
Learn more about the speed of light here;
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