Question

Speed of light in water & in glass is 2.2 × 10 raise to 8 m/s & 2 ×10 raise to 8 respectively , Find Refractive index of ,
i) water with respect to glass .
ii) glass with respect to water ?​

Answer 1

Answer:

Speed of light in water = 2.2 ×108m/s. Therefore, Vw = 2.2 ×108m/s. Now it is also given that speed of light in glass = 2 ×108m/s. Therefore, Vg = 2 ×108m/s.

Answer 2

Analysis→

Here the question conveys that the speed of light in water is $\rm{2.2\times10^8\frac{m}{s}}$ and in glass is $\rm{2\times10^8\frac{m}{s}}$ . And we've to find the Refractive Index of ☞

i) Water with respect to glass.

ii) Glass with respect to water.

So let the refractive index of water be $\rm{\mu _w}$ , speed of light in water be $\rm{v_w}$ and let the refractive index of glass be $\rm{\mu _g}$ , speed of light in glass be $\rm{v_g}$ And we know that :

$\dashrightarrow\bf{v=\dfrac{c}{\mu}}$

Where :-

$\bf{v=speed\:of\:light\:in\:a\:medium}$

$\bf{c=speed\:of\:light\:in\:a\:vacuum\big(3\times10^8\frac{m}{s}\big)}$

$\bf{\mu=refractive\:index\:of\:that\:medium}$

Given→

• $\rm{v_w=2.2\times10^8\frac{m}{s}}$
• $\rm{v_g=2\times10^8\frac{m}{s}}$
• $\rm{c=3\times10^8\frac{m}{s}}$

To Find→

$\rm{^w\mu _g\big(Refractive\:index\:of\:water\:with\:respective\:to\:glass\big)}$

$\rm{^g\mu _w\big(Refractive\:index\:of\:glass\:with\:respective\:to\:water\big)}$

Answer→

❑ First let's find the equation for the relation between the refractive indices of the mediums :)

$\large\implies\rm{v=\dfrac{c}{\mu}}$

$\large\implies\rm{\mu=\dfrac{c}{v}}$

$\large\implies\sf{\mu_w=\dfrac{c}{v_w}\dots\:(i)}$

$\large\implies\sf{\mu_g=\dfrac{c}{v_g}\dots\:(ii)}$

Dividing (i) and (ii) →

$\large\implies\rm{\dfrac{\mu_w}{\mu_g}=\dfrac{\frac{c}{v_w}}{\frac{c}{v_g}}}$

$\large\implies\rm{\dfrac{\mu_w}{\mu_g}=\dfrac{\frac{\cancel{c}}{v_w}\times v_g}{\cancel{c}}}$

$\large\implies\bf{\dfrac{\mu_w}{\mu_g}=\dfrac{v_g}{v_w}}$

★ Now we've find the suitable equation for relation between the refractive indices of the two mediums, so let's put the value of the given data to find there refractive index »

$\large\implies\rm{\dfrac{\mu_w}{\mu_g}=\dfrac{v_g}{v_w}}$

$\large\implies\rm{^w\mu _g=\dfrac{v_w}{v_g}}$

$\large\implies\rm{^w\mu _g=\dfrac{2.2\times10^8\frac{m}{s}}{2\times10^8\frac{m}{s}}}$

$\large\implies\rm{^w\mu _g=\dfrac{2.2\times{\cancel{10^8\frac{m}{s}}}}{2\times{\cancel{10^8\frac{m}{s}}}}}$

$\implies\rm{^w\mu _g=\dfrac{2.2}{2}}$

$\implies\rm{^w\mu _g=\dfrac{\cancel{2.2}}{\cancel{2}}}$

$\implies\rm{^w\mu _g=1.1}$

${\boxed{\boxed{\implies{\bf{^w\mu _g=1.1\checkmark}}}}}$

➫ Hence the refractive index of water with respect to glass is 1.1 which is the required answer $\Large{\checkmark}$

❑ Now let's find the refractive index of glass with respect to water :)

$\large\implies\rm{\dfrac{\mu_g}{\mu_w}=\dfrac{v_w}{v_g}}$

$\large\implies\rm{^g\mu _w=\dfrac{v_g}{v_w}}$

$\large\implies\rm{^g\mu _w=\dfrac{2\times10^8\frac{m}{s}}{2.2\times10^8\frac{m}{s}}}$

$\large\implies\rm{^g\mu _w=\dfrac{2\times{\cancel{10^8\frac{m}{s}}}}{2.2\times{\cancel{10^8\frac{m}{s}}}}}$

$\implies\rm{^g\mu _w=\dfrac{2}{2.2}}$

$\implies\rm{^g\mu _w=\dfrac{\cancel{2}}{\cancel{2.2}}}$

$\implies\rm{^g\mu _g=0.909}$

${\boxed{\boxed{\implies{\bf{^g\mu _w=0.909\checkmark}}}}}$

➫ Hence the refractive index of glass with respect to water is 0.909 which is the required answer $\Large{\checkmark}$

Know More →

❑ Refractive index of some mediums »

$\boxed{\begin{tabular}{c | 1} Material Medium & Refractive Index(n) \\ \cline{1-2} Air & 1.0003 \\ Water & 1.33 \\ Ice & 1.31 \\ Alcohol & 1.36 \\ Kerosene & 1.44 \\ Fused Quartz & 1.46 \\ Crown Glass & 1.52 \\ Rock salt & 1.54 \\ Dense Flint Glass & 1.65 \\ Ruby & 1.71 \\ Diamond & 2.42 \end{tabular}}$

$\Large\maltese{\underline{\underline{\bf{Request\leadsto}}}}$

View the answer in website to see the tabular coding and proper display of the answer :)

HOPE IT HELPS.