Glass and water have a refractive 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 a hypothetical tube of 40,000 km half filled with water and other half filled with glass. Take 'c' = 3 x 10^8 m/s.
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Answer:
refractive index of glass wrt water = 1.13
total time taken = 0.19 s
Explanation:
refractive index of water = n1 = 1.34
refractive index of glass = n2 = 1.52
refractive index of glass wrt water
= 1n2 = n2/n1
= 1.52 / 1.34 = 1.134 = 1.13
speed of light in a medium of refractive index n = v = C / n
distance in each medium = d = 40000/2 = 20000 km
speed in water = v1 = C/n1
speed in glass = v2 = C/n2
time taken = d/v1 + d/v2
= d ( 1/v1 + 1/v2)
= d ( n1/C + n2/C)
= d(n1 + n2) /C
= 20000×10^3 ( 1.34 + 1.52) / (3×10^8)
= 2 × 2.86 / 30
= 0.19 s
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