Question

A light ray is travelling through the cross-section of an optical fibre. The optical fibre is made of four different glasses, but each part has the same geometric thickness. Their respective refractive index are shown in figure. In which part of the fibre, light will take maximum time to cross?

• A. Part I
• B. Part II
• C. Part IV
• D. Part III

Answer 1

The correct option is C Part IV

Refractive index, $\mu =\frac{c}{v}$
where $v$ is velocity of light in medium and $c$ is velocity of light in vacuum.
$c=3\times {10}^8\text{m/s}=\text{constant}$
$\Rightarrow v$ ∝ $\frac{1}{\mu }$
The order of the given refractive index is
IV > III > II > I
Hence, order of speed of light in different parts,
$v_{IV}<v_{III}<v_{II}<v_I$ where $v_I,v_{II}{v}_{III}$ and $v_{IV}$ is velocity of light in medium I, II, III and IV respectively.
$\therefore$ Light will take maximum time in crossing part IV

Why this question? Tip: Time taken to cross the material will be maximum, if light has minimum velocity in that material.