The refractive index of water with respect to vacuum is 4/3 and refractive index of vacuum with respect to glass is .

Question

The refractive index of water with respect to vacuum is \(\frac43\)and refractive index of vacuum with respect to glass is \(\frac23\). If the speed the speed of light in glass is 2 × 10⁸ ms^-1 , find the speed of light in (i) vacuum, (ii) water.

Answer 1

Given; 

Refractive index of (R.I) water w.r.t vacuum = \(\frac43\)

Refractive index (R.I) of vacuum w.r.t glass = \(\frac23\)

Refractive index (R.I) of glass to vacuum will be = \(\frac32\)

Refractive index of glass to water = \(\frac{R.I\,of\,glass}{R.I\,of\,water}= \frac{\frac32}{\frac43}\)

⇒ Refractive index of glass w.r.t water = \(\frac{3\times3}{4\times2}= \frac98\)

⇒ \(\frac{speed\,of\,light\,in\,water}{speed\,of\,light\,in\,glass}= \frac98\)

⇒ \(\frac{speed\,of\,light\,in\,water}{2\times10^8}= \frac98\)

⇒ Speed of light in water = \(\frac{9\times2\times10^8}{8}\)

⇒ Speed of light in water = \(\frac{9\times10^8}{4}\) = 2.25 x 10⁸

Thus, speed of light in water = 2.25 × 10⁸

Refractive index of water w.r.t vacuum = vμw = \(\frac43\)

⇒ \(\frac{speed\,of\,light\,in\,vacuum}{speed\,of\,light\,in\,water}= \frac43\)

⇒ \(\frac{speed\,of\,light\,in\,vacuum}{2.25\times10^8}= \frac43\)

 ⇒ Speed of light in water = \(\frac{4\times2.25\times10^8}{3}\)

⇒ Speed of light in water = \(\frac{9\times10^8}{3}\) 

Thus, speed of light in vacuum is 3 × 10⁸ m/s.