Question

The speed of light in water and glass is $2.2 \times {10^8}m/s$ and $2 \times {10^8}m/s$ respectively. What is the refractive index of glass w.r.t water?

$$(a){\text{ 1}} \\\ (b){\text{ 1}}{\text{.1}} \\\ (c){\text{ 0}}{\text{.909}} \\\ (d){\text{ 0}}{\text{.8}} \\\$$

Answer 1

Hint – In this question use the direct relationship between speed of light in air, speed of light in the given medium and the refractive index that is $V = \dfrac{C}{\mu }$. Use them for two different mediums, that is water and glass. This will help get the refractive index of glass with respect to the water.

Step-By-Step answer:
Given data:
Speed of light in water = 2.2 $\times {10^8}$m/s.
Let it is denoted by ${V_w}$
Therefore, ${V_w}$ = 2.2 $\times {10^8}$m/s.
Now it is also given that speed of light in glass = 2 $\times {10^8}$m/s.
Let it is denoted by ${V_g}$
Therefore, ${V_g}$ = 2 $\times {10^8}$m/s.
Let the refractive index of the water be ${\mu _w}$ and the refractive index of the glass be ${\mu _g}$.
Now we all know the relation of speed of light in any medium when comes from air it is given as,
$\Rightarrow V = \dfrac{C}{\mu }$
Where, V = Speed of light in the medium
c = Speed of light in air or vacuum = $3 \times {10^8}$ m/s.
$\mu$ = refractive index of the medium.
Now the speed of light in the water is given as
$\Rightarrow {V_w} = \dfrac{C}{{{\mu _w}}}$...................... (1)
And the speed of light in the glass is given as
$\Rightarrow {V_g} = \dfrac{C}{{{\mu _g}}}$...................... (2)
Now divide equation (2) from equation (1) we have,
$\Rightarrow \dfrac{{{V_g}}}{{{V_w}}} = \dfrac{{\dfrac{C}{{{\mu _g}}}}}{{\dfrac{C}{{{\mu _w}}}}} = \dfrac{{{\mu _w}}}{{{\mu _g}}}$
Now substitute the values of speed of light in water and the glass we have,
$\Rightarrow \dfrac{{2 \times {{10}^8}}}{{2.2 \times {{10}^8}}} = \dfrac{{{\mu _w}}}{{{\mu _g}}}$
Now simplify this we have,
$\Rightarrow \dfrac{{{\mu _w}}}{{{\mu _g}}} = \dfrac{2}{{2.2}} = 0.909$
$\Rightarrow {\mu _w} = 0.909{\mu _g}$
So the refractive index of glass with respect to the water is 0.909.
So this is the required answer.
Hence option (C) is the correct answer.

Note – In general the refractive index is simply used to measure the concentration of solute in an aqueous solution. It therefore plays a major role in differentiating two different concentrations for two different aqueous mediums. A higher refractive index will allow slower passage of light through it.