Question

If the refractive index of ruby for light going from air to ruby will be \[1.71\] . What will be the refractive index for light going from ruby to air?
A) \[1.71\]
B) \[0.58\]
C) \[0.66\]
D) \[1\]

Answer 1

Hint: Refractive Index is a measure of the bending of a ray of light when passing from one medium to the other. It is a dimensionless number that tells us how fast light travels in a certain medium. Refractive index is usually used to identify a particular substance, confirm its purity or measure its concentration.

Complete step by step solution:
Refractive index of one medium with respect to the second medium is the ratio of speed light in the second medium to the speed of light in the first medium.
Applying the same to the question at hand, we can say that
Since light is travelling from air to ruby, the refractive index of ruby with respect to air will be the ratio of the speed of light in air to the speed of light in ruby.
We can mathematically express this as \[{{\mu }_{ruby}}=\dfrac{{{v}_{air}}}{{{v}_{ruby}}}\] where \[{{\mu }_{ruby}}\] is the refractive index of ruby with respect to air, \[{{v}_{air}}\] is the speed of light in air and \[{{v}_{ruby}}\] is the speed of light in ruby.
Substituting the values in the above equation we get,
\[\begin{align}
  & 1.71=\dfrac{3\times {{10}^{8}}}{{{v}_{ruby}}} \\
 & \Rightarrow {{v}_{ruby}}=\dfrac{3\times {{10}^{8}}}{1.71} \\
 & \Rightarrow {{v}_{ruby}}=1.75\times {{10}^{8}} \\
\end{align}\]
Now we have to consider the inverse of this situation, that is, light is going from ruby to air.
So the refractive index of air with respect to ruby will be equal to the ratio of the speed of light in ruby to the speed of light in air.
Mathematically, we can express this as \[{{\mu }_{air}}=\dfrac{{{v}_{ruby}}}{{{v}_{air}}}\] where \[{{\mu}_{air}}\] is the refractive index of air with respect to ruby and the other terms have the same meaning as before.
Substituting the values now, we get
\[\begin{align}
  & {{\mu}_{air}}=\dfrac{1.75\times {{10}^{8}}}{3\times {{10}^{8}}} \\
 & \Rightarrow {{\mu}_{air}}=0.583\overline{3}\simeq 0.58 \\
\end{align}\]

Hence option (B) is the correct option.

Note:Alternatively, we can use a simple relation to solve the question at hand. The relation says that for a given pair of media, \[\mu _{1}^{2}\times \mu _{2}^{1}=1\] where \[\mu_{1}^{2}\] is the refractive index of the second medium with respect to the first and \[\mu _{2}^{1}\] is the refractive index of the first medium with respect to the second.