The speed of light in glass [tex]1.97 \times 10^{8}\ \mathrm{m} / \mathrm{s}[/tex]
The speed of light in Ruby is [tex]1.75 \times 10^{8} \mathrm{m} / \mathrm{s}[/tex]
The refractive index of air with respect to glass is 0.666
Explanation:
The refractive index is the degree of diffraction of a light beam passing from one medium to another. It can also be defined as the ratio of the speed of light in an empty space to the speed of light in a material. The equation is given as
[tex]\text {refractive index, n\ or } \mu=\frac{\text c}{\text {v}}[/tex]
Given data:
[tex]\mu_{\text {glass}}=1.52[/tex]
[tex]\mu_{r u b y}=1.71[/tex]
Velocity of light in vacuum, c = [tex]3 \times 10^{8} \mathrm{m} / \mathrm{s}[/tex]
We need to find velocity of glass, ruby and refractive index ratio of air and glass
To find velocity of glass,
[tex]1.52=\frac{3 \times 10^{8}}{\text {velocity of glass}}[/tex]
[tex]\text {velocity of glass}=\frac{3 \times 10^{8}}{1.52}=1.97 \times 10^{8} \mathrm{m} / \mathrm{s}[/tex]
To find velocity of ruby,
[tex]1.71=\frac{3 \times 10^{8}}{\text {velocity of Ruby}}[/tex]
[tex]\text {velocity of Ruby}=\frac{3 \times 10^{8}}{1.71}=1.75 \times 10^{8}\ \mathrm{m} / \mathrm{s}[/tex]
To calculate the refractive index of air with respect to glass: = [tex]\frac{\mathrm{n}_{\text {air}}}{\mathrm{n}_{\text {glass}}}[/tex]
We know, the value of the refractive index of air is 1
The value of the refractive index of glass is 1.5
So, the ratio of them should be [tex]\frac{1}{1.5}=0.666[/tex]
