Q. Air has refractive index 1.003, the thickness of air column, which will have one more wave length of yellow light (6000 $\mathring{\mathrm{A}}$) than in the same thickness of vacuum is
A) 2 mm
B) 2 cm
C) 2 m
D) 2 km
Explanation
(a) $\mu_{v} = 1\ and\ \mu_{a} = 1.003$
$\therefore\ \ \ \ \frac{\lambda_{v}}{\lambda_{a}} = \frac{\mu_{a}}{\mu_{v}} = 1.0003$
$x = \lambda_{v}n = \lambda_{a}(n + 1)$
$\frac{n + 1}{n} = \frac{\lambda_{v}}{\lambda_{a}} = 1.0003$
$1 + \frac{1}{n} = 1.0003,\frac{1}{n} = 0.0003$
$n = \frac{1}{0.0003} = \frac{10^{4}}{3}$
$\therefore\ \ x = \lambda_{a}n = 6000 \times 10^{- 7}mm \times \frac{10^{4}}{3} = 2\ mm$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.