Question

Optical path of a monochromatic light is same if it goes through $4.5cm$ of glass or $5.0cm$ in a liquid, the refractive index of the liquid is

• A. $1.33$
• B. $1.35$
• C. $1.45$
• D. $1.67$

Answer 1

The correct option is B $1.35$

We know that $\mu c=$ constant $\{\mu =$ refractive index $\begin{array}{cc}u& =\text{length of medium}\}\\ \text{so,}{\mu }_1{\mu }_1& ={\mu }_2{\mu }_2\end{array}$

${\mu }_1=$ Refractive index of $g/3s=1.53$

${\mu }_1=$ length of glass = $4cm$

${\mu }_2=$ length of water $=4.5$

$\begin{array}{cc}\Rightarrow {\mu }_2=\frac{{\mu }_1{\mu }_1}{{\mu }_2}& =\frac{1.53\times 4}{4.5}\\ & =1.36\\ & \simeq 1.35\end{array}$

$\therefore$ Option (B) is correct.