Question

Glass and water have a reflective index of 1.52 and 1.34 respectively. What is the refractive index of glass with respect to water? How much time will light take to pass through hypothetical tube of 40,000 km half filled with water and other half filled with glass. Take C = 3×10⁸ m/s .

Answer 1

Refractive index of glass w.r.t. water = (Refractive index of glass ) / (Refractive index of water )
=1.52/1.34
=1.13
Refractive index of a medium, nm = Speedoflightinvacuum/Speedoflightinthemedium

Speed of light in vacuum, c=3×108ms−1
Refractive index of glass, ng=1.52



Speed of light in the glass, v = Speedoflightinvacuum/Refractiveindexofglass

v =c/n

g

v =3×108/1.50

=
2×108ms−1

Therefore, speed of light in the glass, v = 2×108ms−1
given that the tube is half filled with glasss
time taken by light to travel through the glass = toatal distance /time
=20000*10^3(half of the tube )m/2*10^8
=10^-1 second

now the case of travel through the water
speed of light in water =speed of light in vaccum / refractive index of water
= 3*10^8/1.34
=2.24*10^8 m/s
now the time taken by the ray to trtavel through the cylinder containing water= distance /time
= 20000*10^3/2.24*10^8
=0.89*10^-1 second

total time taken by the light to travel through the hypothetical cylinder = 1*10^-1 +0.89*10^-1
= [1+0.89]*10^-1
= 1.89*10^-1 seconds