What is the time taken by light to cross a glass 2 mm thick? (Refractive index of glass = 1.5)

A. 10^-10 s
B. 10^-12 s
C. 10^-11 s
D. 10^-9 s

We are tasked to calculate the time taken by light to cross a 2 mm thick glass slab. The refractive index of glass is given as n=1.5n = 1.5.
1. Relationship Between Speed of Light and Refractive Index: The speed of light in a medium is related to the refractive index by:
v=cnv = \frac{c}{n}
Where:
o c=3×108 m/sc = 3 \times 10^8 \, \text{m/s} is the speed of light in vacuum.
o n=1.5n = 1.5 is the refractive index of the glass.
Substituting the values:
v=3×1081.5=2×108 m/sv = \frac{3 \times 10^8}{1.5} = 2 \times 10^8 \, \text{m/s}
2. Time Taken to Cross the Glass: The time taken (tt) for light to travel a distance (dd) in the glass is:
t=dvt = \frac{d}{v}
Here:
o d=2 mm=2×10−3 md = 2 \, \text{mm} = 2 \times 10^{-3} \, \text{m}
o v=2×108 m/sv = 2 \times 10^8 \, \text{m/s}
Substituting the values:
t=2×10−32×108t = \frac{2 \times 10^{-3}}{2 \times 10^8}
Simplify:
t=10−11 st = 10^{-11} \, \text{s}
The time taken by light to cross the glass is:
C) 10−11 s10^{-11} \, \text{s}.