Question

If ratio of refractive indeces of two transparent media is 4:5.What is the ratio of speeds of light in them ?

Answer 1

$\huge\underline\blue{\sf Answer :}$

$\large\red{\boxed{\sf v_1:v_2=5:4}}$

$\large\underline\pink{\sf Given: }$

• Ratio of refractive index ($\bf{{\frac{\mu_1}{\mu_2}}) or \mu_1 : \mu_2}$=4:5

$\large\underline\pink{\sf To\:Find: }$

• Ratio of speeds of light ($\bf{{\frac{v_1}{v_2}})\:or\:v_1:v_2}$=?

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We know that ,

$\large{\boxed{\sf \mu={\frac{c}{v}}}}$

$\large{\sf \mu = Refractive\: index}$

c = speed of light = 3 × 10^8 m/s

v = Speed of light in medium = ?

On Putting value :

$\large{\sf \mu_1={\frac{c}{v_1}} }$

$\large\implies{\sf 4={\frac{3×10^8}{v_1}}}$

$\large\implies{\sf v_1={\frac{3×10^8}{4}}}$

$\large\implies{\sf v_1=0.75×10^8m/s}$

$\large{\sf \mu_2={\frac{c}{v_2}} }$

$\large\implies{\sf v_2={\frac{3×10^8}{5}}}$

$\large\implies{\sf v_2=0.6×10^8m/s}$

Ratio of $\sf{v_1}$ and $\sf{v_2}$ :-

$\large\implies{\sf {\frac{v_1}{v_2}}={\frac{0.75×10^8}{0.6×10^8}} }$

$\large\implies{\sf {\frac{v_1}{v_2}}={\frac{5}{4}}}$

$\huge\red{♡}$$\Large\red{\boxed{\sf v_1:v_2=5:4}}$

Hence ,

Ration of $\sf{v_1}$and $\sf{v_2}$ is 5:4