(C) The angular width of the central maximum in a Fraunhofer diffraction pattern is given by the formula: $\theta = \frac{2 \lambda}{a}$,where $\lambd

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(C) The angular width of the central maximum in a Fraunhofer diffraction pattern is given by the formula: $\theta = \frac{2 \lambda}{a}$,where $\lambda$ is the wavelength of light and $a$ is the slit width.From this relation,we can see that $\theta \propto \lambda$.Let the initial wavelength be $\lambda_1 = 6000 Å$ and the initial angular width be $\theta_1$.When the wavelength is changed to $\lambda_2$,the angular width becomes $\theta_2 = \theta_1 - 0.20 \theta_1 = 0.80 \theta_1$.Using the proportionality $\frac{\theta_2}{\theta_1} = \frac{\lambda_2}{\lambda_1}$,we get:$\frac{0.80 \theta_1}{\theta_1} = \frac{\lambda_2}{6000 Å}$$0.80 = \frac{\lambda_2}{6000 Å}$$\lambda_2 = 0.80 \times 6000 Å = 4800 Å$.

Class 12 Physics Wave Optics Fresnel distance, Diffraction through circular slit, concept of Airy Disc, Rayleigh Criterion of Resolution , Fraunhofer diffraction

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The angular separation of the central maximum in the Fraunhofer diffraction pattern is measured. The slit is illuminated by light of wavelength $6000 Å$. If the slit is illuminated by light of another wavelength,the angular separation decreases by $20 \%$. The wavelength of light used is (in $Å$)

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A
$6400$
B
$5600$
C
$4800$
D
$4400$

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Wave Optics

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Fresnel distance, Diffraction through circular slit, concept of Airy Disc, Rayleigh Criterion of Resolution , Fraunhofer diffraction

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The angular separation of the central maximum in the Fraunhofer diffraction pattern is measured. The slit is illuminated by light of wavelength $6000 Å$. If the slit is illuminated by light of another wavelength,the angular separation decreases by $20 \%$. The wavelength of light used is (in $Å$)

Similar Questions

In Fraunhofer diffraction pattern, slit width is $0.2 \, mm$ and screen is at $2 \, m$ away from the lens. If wavelength of light used is $5000 \, \mathring{A}$, then the distance between the first minimum on either side of the central maximum is (assume $\theta$ is small and measured in radians).

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