A light pulse is sent through a glass slab of thickness 30 cm . It is observed that the light takes 0.5 ns longer to travel through the slab than it would take to travel the same distance in a vacuum. If the speed of light in vacuum is 3 10^8 m/s , the refractive index of the glass slab is:

Step-by-step solution

Let the thickness of the glass slab be d = 30 cm = 0.3 m . The time taken by light to travel through the glass slab is t_ glass = d c , where is the refractive index of the glass. The time taken to travel the same distance in vacuum is t_ vac = d c . The extra time taken is given by: t = t_ glass - t_ vac = d c - d c = ( - 1)d c Rearranging for , we get: - 1 = c t d Substitute the given values ( c = 3 10^8 m/s , t = 0.5 10⁻⁹ s , d = 0.3 m ): - 1 = 3 10^8 0.5 10⁻⁹ 0.3 = 0.15 0.3 = 0.5 = 1 + 0.5 = 1.5 Answer: 1.5