Question

Refractive indices of media A,B,C,D are given below: A: 1.03, B: 1.54, C: 1.71 and D: 2.42. (i) In which of these four media is the speed of light minimum. (ii) Find refractive index of medium D w.r.t. medium A. *

Answer 1

$\underline{\blacksquare\:\:\:\footnotesize{\red{Figure}}}$

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$\underline{\blacksquare\:\:\:\footnotesize{\red{AnsweR}}}$

• $\footnotesize{\text{let , the refractive index of medium A is = }\:\mu_a}$

• $\footnotesize{\text{and , the refractive index of medium B is = }\:\mu_b}$

• $\footnotesize{\text{and , the refractive index of medium C is = }\:\mu_c}$

• $\footnotesize{\text{and , the refractive index of medium D is = }\:\mu_d}$

$\therefore\:\:\footnotesize{\text{velocity of light in medium A is ,}\:\red{v_a=\dfrac{c}{\mu_a}}}$

$\therefore\:\:\footnotesize{\text{velocity of light in medium B is ,}\:\red{v_b=\dfrac{c}{\mu_b}}}$

$\therefore\:\:\footnotesize{\text{velocity of light in medium C is ,}\:\red{v_c=\dfrac{c}{\mu_c}}}$

$\therefore\:\:\footnotesize{\text{velocity of light in medium A is ,}\:\red{v_d=\dfrac{c}{\mu_d}}}$

$\footnotesize{\text{as ,}\:\mu_a<\mu_b<\mu_c<\mu_d }$

$\footnotesize{\text{so ,}\:\dfrac{c}{\mu_a}>\dfrac{c}{\mu_b}>\dfrac{c}{\mu_c}>\dfrac{c}{\mu_d}}$

$\footnotesize{\text{where, c = speed of light in vacuum =}\:3\times10^8\:m.s^{-1}}$

$\therefore\:\:\boxed{\footnotesize{v_a>v_b>v_c>v_d }}$

$\therefore\:\:\red{\footnotesize{\text{Speed of the light is minimum in medium A .}}}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\linethickness{3 mm}\put(1,1){\line(1,0){6.8}}\end{picture}$

$\red{\footnotesize{\text{Refractive index of medium D w.r.t. medium A is , }}}$

$\therefore\:\:\footnotesize{a\mu_d=\dfrac{\mu_d}{\mu_a}}$

$\implies\:\:\footnotesize{a\mu_d=\dfrac{2.42}{1.03}}$

$\implies\:\:\boxed{\red{\footnotesize{a\mu_d=2.35\:\:\:\:(almost)}}}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\linethickness{5.8 mm}\put(1,1){\line(1,0){6.8}}\end{picture}$

Answer 2

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