Explanation:
Formula for path difference is as follows.
x = 2tn
and, refractive index (n) = [tex]\frac{\lambda}{2t}[/tex]
Thickness is calculated as follows.
Thickness (t) = [tex]\frac{volume}{area}[/tex]
Area = [tex]\pi r^{2}[/tex]
= [tex]\pi \times (\frac{d}{2})^{2}[/tex]
= [tex]\frac{0.49 \times 10^{-6}}{3.14 \times 0.01 m}[/tex]
= [tex]1.56 \times 10^{-8}[/tex] m
Now, the refractive index will be calculated as follows.
For drop, n = [tex]\frac{\lambda}{2t}[/tex]
For B drop, n = [tex]\frac{\lambda}{26t}[/tex]
So, n = [tex]\frac{640 \times 10^{-9}}{26 \times 1.56 \times 10^{-8}}[/tex]
= [tex]\frac{640 \times 10^{-9}}{40.56 \times 10^{-8}}[/tex]
= 1.5
Thus, we can conclude that index of refraction of the oil is 1.5.
