Question

In Young's double-slit experiment, the distance between slits and the screen is $1m$ and monochromatic light of wavelength $600nm$ 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. $2mm$
• 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 ${\theta }_0=\frac{\beta }{D}=\frac{\lambda }{d_0}$
$d_0=\frac{\lambda }{{\theta }_0}=\frac{600\times 10^{-9}}{\left(\frac{1}{60}\times \frac{\pi }{180}\right)}$
$d_0=\frac{600\times 60\times 180\times 10^{-9}}{\pi }m=2\text{mm}$