Question

If refractive index of a slab varies as $m=1+x^2$ is measured from one end, then optical path length of a slab of thickness 1 m is

• A. (4/3) m
• B. (3/4) m
• C. 1 m
• D. None of these

Answer 1

Answer: (A)

(4/3) m

As the refractive index of a slab is continuous, the optical path length for $1m$ thick glass slab is given by

${\int }_0^{1}1+x^{2}dx=x+\frac{x^3}{3}{|}_0^1=1+\frac{1}{3}-(0+0)=\frac{4}{3}m$