Question

Monochromatic light of wavelength 477 nm from a distant source passes through a slit that is 0.0310 mm wide. In the resulting diffraction pattern, the intensity at the center of the central maximum (θ = 0∘) is 1.28×10−4 W/m2 .

What is the intensity at a point on the screen that corresponds to θ = 1.20∘. Express your answer to three significant figures and include the appropriate units.

Answer 1

Lets. Monochromatic light of wavelength 477 nm=477×10^-9 m

and the intensity at the center of the central maximum (θ = 0∘) is 1.28×10−4 W/m²

according to Fraunhofer conditions

where A = π a sin(θ)/λ

we calculate the value of A,

A = π a sin(θ)/λ

A = π * 0.0310×10^-3 * sin(1.2º) / (477×10^-9)

A=4.2737 ...........................................(3)

put the value of A on equation number (2)

I = 1.28×10^-4 * sin² (4.2737) / (4.2737)²

I = 3.892×10^-8 W/m²

I =3.89×10^-8 W/m²

the intensity at a point on the screen that corresponds to θ = 1.20∘ IS = I =3.89×10^-8 W/m²