Question

A beam of light of wavelength 400 nm falls on a narrow slit and the resulting diffraction pattern is observed on a screen 2 m away from the slit. It is observed that 2nd order minima occurs at a distance of 2 mm from the position of central maxima. Find the width of hte slit.

Answer 1

Given, `lambda=400nm=400xx10^(-9)m`
`D=2m, y=2mm=2xx10^(-3)m`

Let point P is the point of second order minima.
Now `sin theta=tan theta approx theta=(2xx10^(-3))/2=10^(-3)`
Let the slit separation be a.
Now, for second order minima `theta=(2lambda)/a=10^(-3)`
`rArr (2xx400xx10^(-9))/a=10^(-3)`
Thus, we obtain `a=0.8mm`