Question

If a distance of $x_1$, in a rarer medium and a distance $x_2$ in a denser medium contain the same number of waves of a given monochromatic light, then the refractive index of the denser medium relative to the rarer medium is :

• A. $\frac{x_2}{x_1-x_2}$
• B. $1-\frac{x_2}{x_1}$
• C. $\frac{x_2}{x_1}$
• D. $\frac{x_1}{x_2}$

Answer 1

Answer: (D)

$\frac{x_1}{x_2}$

Using
${\mu }_1{d}_1={\mu }_2{d}_2$

${\mu }_d\times x_2={\mu }_r\times x_1$

$\frac{{\mu }_d}{{\mu }_r}=\frac{x_1}{x_2}$

${}_r{\mu }^d=\frac{x_1}{x_2}$

$\therefore$ Refractive index of denser medium relative to rarer $=\frac{x_1}{x_2}$