Question

In a Young's double slit experiment, the angular width of a fringe formed on a distant screen is $1^{\circ}$. The slit separation is $0.01\, mm$. The wavelength of the light is

• A. $0.174\, nm$
• B. $0.174 \mathring{A}$
• C. $0.174 \,\mu m$
• D. $0.174 \times 10^{-4}\,m$

Answer 1

Answer: (C)

Angular fringe width,
$\theta = \frac{\lambda}{d}$
$ \therefore \lambda = \theta d $
Here, $d = 0.01\, mm$
$ = 10^{-5} \,m, \theta = 1^{\circ} $
$= \frac{\pi}{180}$ radians
$ \lambda = \frac{\pi}{180}\times10^{-5} $
$= 1.74 \times10^{-7} m$
$= 0.174 \times10^{-6} m $
$= 0.174 \mu m$