Question

Yellow light from atomic sodium with a wavelength of $589\, nm$ illuminates a single-slit. The dark fringes in the diffraction pattern are found to be seperated on either side of central bright by $2.2\, mm$, on a screen $1.0\, m$ from the slit. The slit width is

• A. 0.7 mm
• B. 0.54 mm
• C. 1.0 mm
• D. 0.24 mm

Answer 1

Answer: (B)

Given, $\lambda=589\, nm =589 \times 10^{-9} m , D=1.0\, m$
Slit width $=d=$ ?
Here, given the distance between two dark fringes (i.e., dark fringes for $m=\pm 1$ )
$=$ width of central maximum $=2 y=2.2\, mm$
or $y=1.1\, mm =1.1 \times 10^{-3} m$
Using, for zero intensities path difference $=m \lambda$,
we have $\frac{d y}{D}=m \lambda$
Slit width i.e., $d=\frac{m \lambda D}{y}=\frac{(1)\left(589 \times 10^{-9} m \right) \times(1.0 m )}{1.1 \times 10^{-3} m }$
$=0.54\, mm$