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

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

Tardigrade Admin · Accepted Answer

Given, λ=589 nm =589 × 10-9 m , D=1.0 m Slit width =d= ? Here, given the distance between two dark fringes (i.e., dark fringes for m=± 1 ) = width of central maximum =2 y=2.2 mm or y=1.1 mm =1.1 × 10-3 m Using, for zero intensities path difference =m λ, we have (d y/D)=m λ Slit width i.e., d=(m λ D/y)=((1)(589 × 10-9 m ) ×(1.0 m )/1.1 × 10-3 m ) =0.54 mm

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

0.7 mm

0.54 mm

1.0 mm

0.24 mm

Q. 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