Two wavelength of sodium light `590 nm` and `596 nm` are used, in turn, to study the diffraction taking placed at a single slit of aperture `2 xx 10^(

Monjur Alahi

Two wavelength of sodium light `590 nm` and `596 nm` are used, in turn, to study the diffraction taking placed at a single slit of aperture `2 xx 10^(-4)m`. The distance between the slit and screen is `1.5 m`. Calculate the separation between the positions of first maxima of diffraction pattern obtained in the two cases.


0 like 0 dislike
1 views
Share with your friends

1 Answers

Salim Ahmed Kawsar

Call

(a) If the width of each slit is comparable to the wavelength of light used, the interference pattern thus obtained in the double-slit experiment is modified by diffraction from each of the two slits
(b) Given that: Wavelength of the light beam,
`lambda_(1)=590 nm=5.9xx10^(-7)m`
Wavelength of another light beam, `lambda-(2)=596nm=5.96xx10^(-7)m`
Distance the slits from the screen `=D=1.5m`
Distance between the two slits `alpha=2xx10^(-4)m`
For the first secondary maxima,
`sintheta=(3lambda_(1))/(2alpha)=(chi_(1))/(D)`
`chi_(1)=(3lambda_(1)D)/(2alpha) and chi_(2)=(3lambda_(2)D)/(2alpha)`
`therefore` Separation between the positions of first secondary maxima of two sodium lines
`chi_(1)-chi_(2)(3D)/(2alpha)(lambda_(2)-lambda_(1))`
`=(3xx1.5)/(2xx2xx10^(-4))(5.96xx10^(-7)-5.9xx10^(-7))`
`=6.75xx10^(-5)m`

0 like 0 dislike
1 views
Talk Doctor Online in Bissoy App
In Fraumhroffer diffraction pattern due to a single slit, the screen is at distance of 100 cm from the slit and slit is illuminated by `lambda=5893Å`.

Correct Answer - A `x=(flambda)/(d)=(100xx5893xx10^(-8))/(0.01)` 0.5893 cm

2 Answers 2 views
Green light of wavelength 5100 Å from a narrow slit is incident on a double slit . If the overall separation of 10 fringes on a screen 200 cm away is

Correct Answer - A `beta=(2)/(10)cm=2xx10^(-3)m` As `beta=(lamdaD)/(d)` `:. d=(lamdaD)/(beta)=(5000xx10^(-10)xx200xx10^(-2))/(2xx10^(-3))` `=5xx10^(-4)m`

2 Answers 1 views
A beam of light of wavelength 600 nm from a distance source falls on a single slit 2 mm wide and the resulting diffraction pattern is observed on a sc

Given, `lambda=600nm, a=2xx10^(-3)m and D=2m` Distance of first dark fringe from centre `y_(1)=(Dlambda)/a` Distance between the first dark fringes on either side of the central bright fringe, `2y_(1)=(2Dlambda)/a=(2xx2xx600xx10^(-9))/(2xx10^(-3))=1200xx10^(-6)m` `=1.2xx10^(-3)m=1.2mm`

2 Answers 1 views
A linear aperture whose width is 0.02 cm is placed immediately in front of a lens of focal length 60cm. The aperture is illuminated normally by a para

Correct Answer - D Ist minima is formed at a distance `Y=(lambdaD)/a` where, `lambda` = wavelength of parallel beams D=focal length a=width of linear aperture `rArrY=((5xx10^(-5))(0.6))/(0.02xx10^(-2))` `rArr Y=0.15 cm`

2 Answers 1 views
Light of wavelength `lambda` is incident on a slit of width d and distance between screen and slit is D. Then width of maxima and width of slit will b

Correct Answer - B In diffraction fringe width `beta=(lambdaD)/d` when `d/2=beta" then"d/2=(lambdaD)/drArrD=d^(2)/(2lambda)`

2 Answers 1 views
In a double slit experiment, the two slits are `1mm` apart and the screen is placed `1m` away. A monochromatic light of wavelength `500nm` is used. Wh

Correct Answer - A Given `d=1mm=1xx10^(-3)mD=1m` `lambda=500nm=5xx10^(-7)m` As width of central maxima = width of 10 maxima `:. (2Dlambda)/a=10((lambdaD)/d)rArra=d/5=10^(-3)/5=0.2xx10^(-3)m` `a=0.2mm`

2 Answers 2 views
A screen is placed 2 m away from a single narrow slit which is illuminated by the light of wavelength `6xx10^(-7)`m. If the first minimum lies 4 mm on

Correct Answer - 0.03 cm

2 Answers 1 views
A parralel beam of monochromatic light of wavelength 5000 Å is incident normally in a narrow slit of width 0.25 mm. The diffraction pattern is observe

Correct Answer - `6xx10^(-3)rad`

2 Answers 1 views
A beam of light of wavelength 590 nm is focused by a convex lens of diameter 10 cm at a distance of 20 cm from it. Find the diameter of the disc image

Correct Answer - `5.6xx10^(-4)`cm

2 Answers 1 views
Sodium light of wavelength 5890 Å is incident normally on a diffraction grating of 5000 rulings per cm. Find the angle of diffraction for the second o

Correct Answer - `36.1^(@)`

2 Answers 2 views
X