Question

In Young's double-slit experiment, the distance between slits and the screen is $1 \, m$ and monochromatic light of wavelength $600 \, nm$ is being used. A person standing near the slits is looking at the fringe pattern. When the separation between the slits is varied, the interference pattern disappears for a particular distance $d_{0}$ between the slits. If the angular resolution of the eye is $\frac{1}{60}^\circ $ , then the value of $d_{0}$ is close to

• A. $1mm$
• B. $3mm$
• C. $2 \, mm$
• D. $4mm$

Answer 1

Answer: (C)

When the angular fringe width in the interference pattern becomes less than the angular resolving power of the person's eye, the fringes will disappear.
The angular fringe width $\theta _{0} = \frac{\beta }{D} = \frac{\lambda }{d_{0}}$
$d_0=\frac{\lambda}{\theta_0}=\frac{600 \times 10^{-9}}{\left(\frac{1}{60} \times \frac{\pi}{180}\right)}$
$d_{0}=\frac{600 \times 60 \times 180 \times 10^{- 9}}{\pi }m=2\text{mm}$