Question

The refractive indices of glycerine and diamond with respect to air are 1.4 and 2.4 respectively. Calculate the speed of light in glycerine and diamond. From these results, calculate the refractive index of diamond with respect to glycerine. (c =3×${{10}^{8}}m/s$)
A. $\text{ }2.14\times {{10}^{8}}m/s;1.25\times {{10}^{8}}m/s;1.714$
B. $0.2143\times {{10}^{8}}m/s;12.5\times {{10}^{5}}m/s;0.1714$
C. $2.143\times {{10}^{6}}m/s;1.250\times {{10}^{3}}m/s;1.74$
D. $21.43\times {{10}^{8}}m/s;0.125\times {{10}^{5}}m/s;17.14$

Answer 1

Hint: Use formula of refractive index in medium. Speed of light is $3\times {{10}^{8}}m/s$ in air only. Refractive index will vary according to medium. Refractive index of air is 1.0003. Refractive index measures bending of light.

Complete step-by-step answer:
 Refractive index: It is nothing but opposition of a medium. It measures how much light slows down, when light travels in medium. It is a ratio of speed of light in air and speed of light in medium. It is nothing but bending of light in a medium.
 We have a refractive index of glycerine with respect to air is 1.4 and the refractive index of diamond with respect to air is 2.4.
Aim: Calculate speed of light(c) in glycine and diamond. Calculate refractive index of diamond with respect to glycerine.
Refractive index is given by,
$\mu =\dfrac{c}{v}$
Where,
$\mu $= refractive index
c = speed of light.
v = speed of medium
Refractive index of glycine is given by,
${{\mu }_{1}}$=1.4
Use formula of refractive index,
${{\mu }_{1}}=\dfrac{c}{{{v}_{1}}}$
Put values
$\begin{align}
  & 1.4=\dfrac{3\times {{10}^{8}}}{{{v}_{1}}} \\
 & {{v}_{1}}=2.14\times {{10}^{8}}m/s \\
\end{align}$
Speed of light in glycerine is ${{v}_{1}}=2.14\times {{10}^{8}}m/s$.
Refractive index of diamond is given by,
${{\mu }_{2}}=2.4$
Use formula of refractive index,
\[{{\mu }_{2}}=\dfrac{c}{{{v}_{2}}}\]
$2.4=\dfrac{3\times {{10}^{8}}}{{{v}_{2}}}$
${{v}_{2}}=1.25\times {{10}^{8}}m/s$
Speed of light in diamond is ${{v}_{2}}=1.25m/s$
Now solve second part,
Calculate refractive index of diamond with respect to glycerine.
\[\begin{align}
  & \mu =\dfrac{{{\mu }_{2}}}{{{\mu }_{1}}} \\
 & \mu =\dfrac{2.4}{1.4} \\
 & \mu =1.714 \\
\end{align}\]
Correct option is (A)

Note: Refractive index do not have units because it is a ratio of two same quantities having the same SI unit. Do not get confused between speed of light and speed of light in the medium. Generally the speed of light is defined as the speed of light in air. Notions may vary but units will be the same.