(C) The radius of the $n^{th}$ Fresnel zone is given by the formula $r_n = \sqrt{n b \lambda}$,where $b$ is the distance from the aperture to the scre

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(C) The radius of the $n^{th}$ Fresnel zone is given by the formula $r_n = \sqrt{n b \lambda}$,where $b$ is the distance from the aperture to the screen and $\lambda$ is the wavelength of light.Given that the radius of the $4^{th}$ zone for wavelength ${\lambda _1}$ is equal to the radius of the $5^{th}$ zone for wavelength ${\lambda _2}$,we have:$r_4 = \sqrt{4 b \lambda_1}$$r_5 = \sqrt{5 b \lambda_2}$Since $r_4 = r_5$,we equate the expressions:$\sqrt{4 b \lambda_1} = \sqrt{5 b \lambda_2}$Squaring both sides,we get:$4 b \lambda_1 = 5 b \lambda_2$Dividing both sides by $b$ (where $b \neq 0$):$4 \lambda_1 = 5 \lambda_2$Therefore,the ratio is:$\frac{\lambda_1}{\lambda_2} = \frac{5}{4}$

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

Medium

In a Fresnel diffraction arrangement,the screen is at a distance of $2 \ m$ from a circular aperture. It is found that for light of wavelengths ${\lambda _1}$ and ${\lambda _2},$ the radius of the $4^{th}$ zone for ${\lambda _1}$ coincides with the radius of the $5^{th}$ zone for ${\lambda _2}.$ Then the ratio ${\lambda _1}:{\lambda _2}$ is

A
$\sqrt {4/5} $
B
$\sqrt {5/4} $
C
$5/4$
D
$4/5$

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Class 12 Questions

Class 12

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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

$A$ light beam of wavelength $800 \,nm$ passes through a single slit and is projected on a screen kept at $5 \,m$ away from the slit. What should be the slit width for the ray optics approximation to be valid (in $\,mm$)?

MediumTS EAMCET 2018

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The angular width of the central maxima in Fraunhofer diffraction for $\lambda = 6000 \; \mathring{A}$ is $\theta_{0}$. When the same slit is illuminated by another monochromatic light,the angular width decreases by $30 \%$. The wavelength of this light is ....... $\mathring{A}$.

MediumNEET 2019

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Find the half-angular width of the central maximum in the Fraunhofer diffraction pattern produced by a slit of width $12 \times 10^{-5} \text{ cm}$,when illuminated by monochromatic light of wavelength $6000 \, \mathring{A}$. (Answer in degrees)

Medium

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In a Fraunhofer diffraction experiment at a single slit using light of wavelength $400 \ nm$,the first minimum is formed at an angle of $30^{\circ}$. The direction $\theta'$ of the first secondary maximum is given by

DifficultKCET 2008

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$A$ single slit Fraunhofer diffraction pattern is formed with white light. For what wavelength of light does the third secondary maximum in the diffraction pattern coincide with the second secondary maximum in the pattern for red light of wavelength $6500 Å$ (in $Å$)?

DifficultKCET 2007

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$A$ light beam of wavelength $800 \,nm$ passes through a single slit and is projected on a screen kept at $5 \,m$ away from the slit. What should be the slit width for the ray optics approximation to be valid (in $\,mm$)?

The angular width of the central maxima in Fraunhofer diffraction for $\lambda = 6000 \; \mathring{A}$ is $\theta_{0}$. When the same slit is illuminated by another monochromatic light,the angular width decreases by $30 \%$. The wavelength of this light is ....... $\mathring{A}$.

Find the half-angular width of the central maximum in the Fraunhofer diffraction pattern produced by a slit of width $12 \times 10^{-5} \text{ cm}$,when illuminated by monochromatic light of wavelength $6000 \, \mathring{A}$. (Answer in degrees)

In a Fraunhofer diffraction experiment at a single slit using light of wavelength $400 \ nm$,the first minimum is formed at an angle of $30^{\circ}$. The direction $\theta'$ of the first secondary maximum is given by

$A$ single slit Fraunhofer diffraction pattern is formed with white light. For what wavelength of light does the third secondary maximum in the diffraction pattern coincide with the second secondary maximum in the pattern for red light of wavelength $6500 Å$ (in $Å$)?

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