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प्रश्न
In a double-slit experiment using the light of wavelength 600 nm, the angular width of the fringe formed on a distant screen is 0.1°. Find the spacing between the two slits.
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उत्तर १
The angular width (θ) of the fringe in the double-slit experiment is given by,
`theta=lambda/"d"`
Where
d = Spacing between the slits
Given:
The wavelength of light, λ = 600 nm
The angular width of the fringe,
θ = 0.1° = `pi/1800` = 0.0018 rad
∴ d = `lambda/theta`
d = `(600xx10^(-9))/(18xx10^(-4))`
d = 0.33 × 10−3 m
उत्तर २
Wavelength of light used, λ = 6000 nm = 600 × 10−9 m
Angular width of fringe, θ = 0.1° =` 0.1 xx pi/180 = 3.14/1800 "rad"`
The angular width of a fringe is related to slit spacing (d) as:
θ = `lambda/"d"`
`"d"= lambda/θ`
= `(600 xx 10^(-9))/(3.14 /1800)`
= 3.44 × 10−4 m
Therefore, the spacing between the slits is 3.44 × 10−4 m.
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संबंधित प्रश्न
(i) In Young's double-slit experiment, deduce the condition for (a) constructive and (b) destructive interferences at a point on the screen. Draw a graph showing variation of intensity in the interference pattern against position 'x' on the screen.
(b) Compare the interference pattern observed in Young's double-slit experiment with single-slit diffraction pattern, pointing out three distinguishing features.
Show that the fringe pattern on the screen is actually a superposition of slit diffraction from each slit.
In a double-slit experiment the angular width of a fringe is found to be 0.2° on a screen placed 1 m away. The wavelength of light used is 600 nm. What will be the angular width of the fringe if the entire experimental apparatus is immersed in water? Take refractive index of water to be 4/3.
In Young's double slit experiment, derive the condition for
(i) constructive interference and
(ii) destructive interference at a point on the screen.
What is the effect on the interference fringes to a Young’s double slit experiment when
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(ii) the width of a source slit is increased?
(iii) the monochromatic source is replaced by a source of white light?
Justify your answer in each case.
The intensity at the central maxima in Young’s double slit experimental set-up is I0. Show that the intensity at a point where the path difference is λ/3 is I0/4.
If the separation between the slits in a Young's double slit experiment is increased, what happens to the fringe-width? If the separation is increased too much, will the fringe pattern remain detectable?
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- Find the minimum value of d so that there is a dark fringe at O.
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(ii) Fringe width, i.e. fringe separation.
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In Young's double-slit experiment, the separation between the two slits is d and the distance of the screen from the slits is 1000 d. If the first minima fall at a distance d from the central maximum, obtain the relation between d and λ.
In Young’s double slit experiment, how is interference pattern affected when the following changes are made:
- Slits are brought closer to each other.
- Screen is moved away from the slits.
- Red coloured light is replaced with blue coloured light.
If the monochromatic source in Young’s double slit experiment is replaced by white light, then ______.
