Question

The speed of light in water and glass is $2.2 \times {10^8}ms^{-1}$ and $2 \times {10^8}ms^{-1}$ respectively. What is the refractive index of the water w.r.t glass?
A) $1.2$
B) $\dfrac{1}{{0.909}}$
C) $1$
D) $0.909$

Answer 1

Hint: The refractive index can be defined as that the refractive index of a medium is equal to the ratio of the velocity of the light in a vacuum to the velocity of the light in that medium.

Formula used:
To find the refractive index of the water w.r.t to glass is,
${\mu _w} = \dfrac{{{V_g}}}{{{V_w}}}$
Where, ${\mu _w}$=Refractive index of water,
${V_w}$=velocity of light in water,
${V_g}$=velocity of light in the glass.

Complete step by step answer:
We know the values of velocity of light in water and glass. So, it is very simple to derive the answer just by applying the values in the formula. We have,
${V_g} = 2 \times {10^8}m{s^{ - 1}}$
${V_w} = 2.2 \times {10^8}m{s^{ - 1}}$
On substituting these values in the known formula,
${\mu _w} = \dfrac{{{V_g}}}{{{V_w}}}$
$\Rightarrow {\mu _w} = \dfrac{{2 \times {{10}^8}}}{{2.2 \times {{10}^8}}}$
$\Rightarrow {\mu _w} = 0.909$

$\therefore $ The refractive index of the water w.r.t glass is 0.909. Hence the correct option is option (D).

Additional information:
i)There are many applications of the refractive index of a specific medium. It is used to measure the concentration of a solute in a given aqueous solution, to identify a particular substance, to confirm the purity of the substance.
ii)The refractive index helps to understand the behavior of light. When the light travels through the medium having a large refractive index, the velocity of light decreases. It is because of the interaction of light with the substrates in that medium. If we increase the temperature in the medium the substrate will be in lesser concentration or else disappears. In that situation, the refractive index of that medium will decrease, hence it leads to the velocity of light to increase.
iii) These refractive indices are also used in finding the concentration of drugs in the pharmaceutical industry.

Note:
The refractive of the medium common formula is, $\mu = \dfrac{c}{v}$, where $c$ is the velocity of light in a vacuum and $v$ is the velocity of light in that medium. You always observe that the refractive index has no units.