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/m^{2}

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} * sin^{2} (4.2737) /
(4.2737)^{2}

I = 3.892×10^{-8} W/m^{2}

I =3.89×10^{-8} W/m^{2}

the
intensity at a point on the screen that corresponds to θ = 1.20∘ IS
= I =3.89×10^{-8} W/m^{2}

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