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The refractive index of water and glass with respect to air are 4/3 and 3/2 respectively. The refractive index of glass with respect to water will be:
1. 9 / 8
2. 8 / 9
3. 9 / 4
4. 3 / 2

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Correct Answer - Option 1 : 9 / 8

Concept:

Refractive index: 

  • The ratio of the speed of light in a vacuum to the speed of light in a medium is called the refractive index of that medium.
  • It is also called an absolute refractive index.

\({\rm{Refractive\;index\;}}\left( μ \right) = {\rm{\;}}\frac{{Speed\;of\;light\;in\;vaccum\left( C \right)}}{{Speed\;of\;light\;in\;a\;medium\left( v \right)}}\)

Calculation:

Given that, \(\mu _w^a = \frac{4}{3} \),\( \mu _g^a = \frac{3}{2} \)

Refractive index of water w.r.t glass = \( \mu _w^g = \frac{{\mu _w^a}}{{\mu _g^a}} = \frac{{\frac{4}{3}}}{{\frac{3}{2}}} = \frac{8}{9} \)

Also,

\( {\mathop{\rm Re}\nolimits} fractive\;index\;of\;water\;w.r.t\;glass = \frac{1}{\begin{array}{l} {\mathop{\rm Re}\nolimits} fractive\;index\;of\;glass\;w.r.t\;water\\ \end{array}}\)

\( {\mathop{\rm Re}\nolimits} fractive\;index\;of\;glass\;w.r.t\;water = \frac{1}{\begin{array}{l} {\mathop{\rm Re}\nolimits} fractive\;index\;of\;water\;w.r.t\;glass\\ \end{array}}\)

\( {\mathop{\rm Re}\nolimits} fractive\;index\;of\;glass\;w.r.t\;water = \frac{1}{{\frac{8}{9}}} = \frac{9}{8} \)

The refractive index of glass with respect to water will be 9/8

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