Question

Speed of light in air is $3\times {{10}^{8}}m/s$ and speed of light in common glass is $2\times {{10}^{8}}m/s$. Refractive index of glass will be:
A. $\dfrac{2}{3}$
B. $\dfrac{1}{2}$
C. $\dfrac{3}{2}$
D. $\dfrac{2}{5}$

Answer 1

Hint: Refractive index of any medium can be given by the formula, $\dfrac{\sin {{\theta }_{1}}}{\sin {{\theta }_{2}}}=\dfrac{{{v}_{1}}}{{{v}_{2}}}=\dfrac{{{n}_{2}}}{{{n}_{1}}}={{n}_{21}}$. Now, using this formula we will find the value of the refractive index of glass by using the values of speed of light in air and speed of light in glass.

Formula used: $\dfrac{\sin {{\theta }_{1}}}{\sin {{\theta }_{2}}}=\dfrac{{{v}_{1}}}{{{v}_{2}}}=\dfrac{{{n}_{2}}}{{{n}_{1}}}={{n}_{21}}$

Complete Step-by-Step solution:
In the question we are given that the speed of light in air and speed of light in glass and by using that we have to find the value of refractive index of glass, this can be done by using the formula,
$\dfrac{\sin {{\theta }_{1}}}{\sin {{\theta}_{2}}} = \dfrac{{{v}_{1}}}{{{v}_{2}}} = \dfrac{{{n}_{2}}}{{{n}_{1}}} = {{n}_{21}}$
Where, ${{\theta }_{1}}$ and ${{\theta }_{2}}$ are angles made by the light in medium 1 and medium 2, ${{v}_{1}}$and ${{v}_{2}}$ are velocities of light in medium 1 and medium 2, ${{n}_{1}}$ and ${{n}_{2}}$ are refractive indices of medium 1 and medium 2.
Here, medium 1 air and medium 2 is glass. And here in the question we are not given angles and refractive indices so, we will ignore that term in the formula, which can be given mathematically as,
$\dfrac{{{v}_{1}}}{{{v}_{2}}}={{n}_{21}}$
Now, replacing ${{v}_{1}}$ as ${{v}_{a}}$and ${{v}_{2}}$ as ${{v}_{g}}$, where ${{v}_{a}}$ and ${{v}_{g}}$ are velocities of light in air and glass respectively, we will get,
$\dfrac{{{v}_{a}}}{{{v}_{g}}}={{n}_{g}}$
$\Rightarrow \dfrac{3\times {{10}^{8}}}{2\times {{10}^{8}}}={{n}_{g}}$
$\Rightarrow {{n}_{g}}=1.5$
Hence, the value of the refractive index of glass is 1.5.

Note: In such types of questions, students must take care about what is given in the question and they should also take care about what is to be considered as medium 1 and medium otherwise the values might get reversed and due to that answer may go wrong.