Question

The speed in light in certain medium is 2/5 of its speed in air. the refractive index of medium is​

Answer 1

Answer:

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Explanation:

Answer 2

Given,

Speed of light in a medium = 2/5 of the speed of light in air.

To find,

Refractive index of the medium.

Solution,

We can solve this numerical problem simply by following the steps given below.

First of all, for solving such problems, we should understand what the refractive index is and how is it calculated.

So, it may be said that the "refractive index is a measure of the bending of a ray of light when passing from one medium into another". It is mathematically defined as "the ratio of the sine of the angle of incidence to the sine of the angle of refraction".

Also, it is defined in a way that, "the ratio of the velocity of light in the empty space (vacuum or air) to that of light in a medium". It is denoted by $n$, or μ.

Let $i,r$ be the angles of incidence and refraction respectively and $c,v$ be the velocities of light in empty space and in medium respectively. Then, the refractive index of the medium is defined as,

$n=\frac{sin(i)}{sin(r)} =\frac{c}{v}.$

Now, the relation between velocities of light in air and the medium is given in the question so we have to use the relation,

$n=\frac{c}{v}$

It is given that speed of light in the given medium $=\frac{2}{5}$ times the speed in empty space. That is,

$v=\frac{2}{5} c$

Simplifying and rearranging,

$\frac{c}{v} =\frac{5}{2}$

Now, since

$n=\frac{c}{v}$

On substituting the value of $c/v$ from the previous expression in the above equation, we obtain,

$n=\frac{5}{2}=2.5$

Or, $n=2.5$.

Therefore, the value of the refractive index for the given medium will be 2.5.