Question

The absolute refractive indices of glass and water are 3/2 and 4/3 respectively determine the ratio of speed of light in glass and water

Answer 1

Answer:

Refractive index of a medium is defined as the ratio of speed of light in vacuum to speed of light in the medium.

given v_g=2 \times 10^8\ m/svg=2×108 m/s  

Let velocity in vacuum = v

refractive index of glass is 3/2. 

(you have given wrong information.)

\begin{lgathered}\eta_g = \frac{v}{v_g} \\ \\ \frac{3}{2}= \frac{v}{2 \times 10^8} \\ \\v= \frac{ 3 \times 2 \times 10^8}{2}= 3 \times 10^8\ m/s\end{lgathered}ηg=vgv23=2×108vv=23×2×108=3×108 m/s 

So speed of light in vacuum is 3 \times 10^8\ m/s3×108 m/s .

\begin{lgathered}\eta_w= \frac{v}{v_w}\\ \\ \frac{4}{3}= \frac{3 \times 10^8}{v_w} \\ \\ v_w= \frac{3 \times 3 \times 10^8}{4} =2.25 \times 10^8\ m/s\end{lgathered}ηw=vwv34=vw3×108vw=43×3×108=2.25×108 m/s 

So speed of light in water is 2.25 \times 10^8\ m/s2.25×108 m/s