Question

The refractive index of rock salt is 1.54 and that of alcohol is 1.36 with respect to air. What is the refractive index of rock salt with respect to alcohol?
\[\begin{align}
  & A)1.31 \\
 & B)1.12 \\
 & C)0.88 \\
 & D)None \\
\end{align}\]

Answer 1

Hint: Refractive index is always calculated by dividing the refractive index of a pair of media. When light is going from one transparent medium to another medium. When we have to find the refractive index of medium A with respect to another medium B then it is calculated by dividing the refractive index of medium with medium B and we get the result.

Complete step-by-step answer:
When a ray of light that travels obliquely from one transparent medium into another medium then ray of light will change its direction in the medium. So Refractive Index of medium gives the information about the extent up to which the change in direction of light ray takes place in a given pair of media.
If medium 1 is vacuum or air, then if the refractive index of medium 2 is considered with respect to medium 1 then it is called the absolute refractive index of the medium 2. It can be written mathematically as-
\[_{1}{{\mu }_{2}}=\dfrac{{{\mu }_{2}}}{{{\mu }_{1}}}\]
Which can be read out as refractive index of medium two with respect to medium1.
The absolute refractive index of a medium is simply called its refractive index.
According to question,
Refractive index of rock salt with respect to air is given 1.54
Let us assume the refractive index of rock salt with respect to air is represented by \[_{a}{{\mu }_{r}}\]
\[\Rightarrow \]\[_{a}{{\mu }_{r}}=1.54\]
Which can be expressed as -
\[\Rightarrow \]\[_{a}{{\mu }_{r}}=\dfrac{{{\mu }_{r}}}{{{\mu }_{a}}}=1.54\] (Equation 1)
Refractive index of Alcohol with respect to air is given as 1.36
Let us assume the refractive index of rock salt with respect to air is represented by \[_{a}{{\mu }_{alco}}\]
\[{{\Rightarrow }_{a}}{{\mu }_{alco}}=\dfrac{{{\mu }_{alco}}}{{{\mu }_{a}}}=1.36\] (Equation 2)
Now we have to find the refractive index of rock salt with respect to alcohol.
Let the assume that refractive index of rock salt with respect to alcohol. is represented by\[_{alco}{{\mu }_{r}}\].
So we can write it as -
\[{{\Rightarrow }_{alco}}{{\mu }_{r}}=\dfrac{{{\mu }_{r}}}{{{\mu }_{alco}}}\]
Now represent each refractive index with respect to air so we get,
\[{{\Rightarrow }_{alco}}{{\mu }_{r}}=\dfrac{_{a}{{\mu }_{r}}}{_{a}{{\mu }_{alco}}}\]
Put the value here from Equation 1 and 2,we get.
\[_{alco}{{\mu }_{r}}=\dfrac{1.54}{1.36}\]
\[{{\therefore }_{alco}}{{\mu }_{r}}=1.13\]

So, the correct answer is “Option A”.

Note: We have to note that by default if another medium is not given we have to consider it with respect to air. Relative refractive index is always represented when the air medium is used. Refractive index of air and medium is almost the same i.e. approximately equal to 1.Refractive index of water is 1.33 and refractive index of glass is 1.5 these are mostly asked values of refractive index.