Question

The index of refraction of glass is 1.52 and that of water is 1.333 . Part A: Compare the speed of light in water with the speed of light in glass. Part B: With respect to the normal, compare the angle of refraction in water with the angle of refraction in glass. Assume refraction is of a light ray entering from the air.

Answer 1

Answer: A) speed of ligth in water=2.25*10^8 m/s

while the speed of ligth in glass =1.97*10^8 m/s

B) sin(θr)=0.75*sin(θi) ( water)

sin(θr)=0.66*sin(θi) ( glass)  

Then sin (θrwater)/(sin (θrglass)=1.14

Explanation: In order to explain this problem we have to consider the expression for speed of light in differents materials, which is given by:

v=c/n where c is the speed of ligth in vacuum and n is the refractive index of the material.

vwater=3*10^8/1.333=2.25*10^8 m/s

vglass=3*10^8/1.53=1.97*10^8 m/s

On the othet hand to calculate the refraction angles in water and glass for the light entering from air we have to take into account the second Snell law which is:

nair*sin (θi)=nwater*sin (θr)

sin (θrwater)= nair/nwater* sin(θi)=0.75*sin (θi)

for the glass

nair*sin (θi)=nglass*sin (θr)

sin (θrglass)= nair/nglass* sin(θi)=0.66*sin (θi)

dividing both we have

sin (θrwater)/(sin (θrglass))=0.75/0.66=1.14

The refraction angle in water is higher than the obtained for the glass.