Angular width of the central maxima in the Fraunhofer diffraction for λ = 6000 mathringA is θ0. When the same slit is illuminated by another monochromatic light, the angular width decreases by 30%. The wavelength of this light is,

Question

Angular width of the central maxima in the Fraunhofer diffraction for λ = 6000 mathringA is θ0. When the same slit is illuminated by another monochromatic light, the angular width decreases by 30%. The wavelength of this light is, (A) 1800 mathringA (B) 4200 mathringA (C) 6000 mathringA (D) 420 mathringA

Tardigrade Admin · Accepted Answer

Angular width propto (λ/d) ⇒ (θ0/0.7θ0) = ((6000 mathringA/d)/(λ)d) ⇒ λ = 4200 mathringA

Q. Angular width of the central maxima in the Fraunhofer diffraction for $λ = 6000 \overset{˚}{A}$ is $θ_{0}$ . When the same slit is illuminated by another monochromatic light, the angular width decreases by 30%. The wavelength of this light is,

$1800 \overset{˚}{A}$

$4200 \overset{˚}{A}$

$6000 \overset{˚}{A}$

$420 \overset{˚}{A}$

Angular width $\propto \frac{λ}{d}$
$\Rightarrow \frac{θ _{0}}{0.7 θ _{0}} = \frac{\frac{6000 A ˚}{d}}{\frac{λ}{d}}$
$\Rightarrow λ = 4200 \overset{˚}{A}$

Q. Angular width of the central maxima in the Fraunhofer diffraction for λ=6000A˚ is θ0​. When the same slit is illuminated by another monochromatic light, the angular width decreases by 30%. The wavelength of this light is,

1800A˚

4200A˚

6000A˚

420A˚