Question

Narrow, equally spaced vertical slits with equal widths are located at a distance of D = 2.17 m from a screen. The intensity pattern in the figure is observed when light with wavelength = 470 nm from a laser passes through the slits, illuminating them uniformly. The screen is perpendicular to the laser beam.

0 1 2 3 4 5 6 7 8 9 cm

Calculate the width of the slits. Use the cm scale to measure distances on the screen.

Answer 1

Given ,

Distance of the screen from the slit D = 2.17m

Wavelength $\lambda$ of the wave = 470nm = 470×10^-9m

Width of the slit = a

Using the formula,

Width of central maximum of diffraction = 2$\lambda$D / a ........eq(1)

From the diagram , width of central maximum = 1 cm = 0.01m

Using eq(1)

0.01 = 2×470×10^-9×2.17 / a

a = 2.04 × 10^-4 m

a = 0.0204 cm