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प्रश्न
State with reason, how the linear width of the central maximum will be affected if
(i) monochromatic yellow light is replaced with red light, and
(ii) distance between the slit and the screen is increased.
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उत्तर १
sin θ =`lambda/a`
where θ is a very small
sin θ = θ
aθ = λ
θ `= lambda/a`
θ `= x/D`
`lambda /a = x/D`
`x = (lambdaD)/a`
width in of central maxima
ω = 2x
`omega = 2x = (2 lambdaD )/a`
(i) `omega = (2 lambda D)/a`
if yellow light replaced by red light its wavelength increases so width will also increase.
(ii) If distance between slit & screen increased width will increase
उत्तर २
For a single slit experiment, the size(angular width) of the central maximum is given by `(2lambda)/"a"`, where a is the slit width.
So the width of the central maximum is directly proportional to the wavelength of light and inversely proportional to slit width.
(i) When monochromatic yellow light is replaced with monochromatic red light, the Width of the central maximum will increase, because the wavelength of red light is more than the wavelength of yellow light.
(ii) When the distance between the slit and the screen is increased, there is no effect on the width of the central maximum, as the width of the central maximum clearly depends only on wavelength and slit width, not on the distance of the screen from the slit.
संबंधित प्रश्न
Two monochromatic rays of light are incident normally on the face AB of an isosceles right-angled prism ABC. The refractive indices of the glass prism for the two rays '1' and '2' are respectively 1.3 and 1.5. Trace the path of these rays after entering the prism.
When light travels from a rarer to a denser medium, the speed decreases. Does this decrease in speed imply a reduction in the energy carried by the wave?
What kind of fringes do you expect to observe if white light is used instead of monochromatic light?
When monochromatic light travels from a rarer to a denser medium, explain the following, giving reasons:
(i) Is the frequency of reflected and refracted light same as the frequency of incident light?
(ii) Does the decrease in speed imply a reduction in the energy carried by light wave?
If a monochromatic source of light is replaced by white light, what change would you observe in the diffraction pattern?
Consider the situation shown in the figure. The two slits S1 and S2 placed symmetrically around the central line are illuminated by a monochromatic light of wavelength λ. The separation between the slits is d. The light transmitted by the slits falls on a screen ∑1placed at a distance D from the slits. The slit S3 is at the central line and the slit S4 is at a distance z from S3. Another screen ∑2 is placed a further distance D away from ∑1.Find the ratio of the maximum to minimum intensity observed on ∑2 if z is equal to
(a) \[z = \frac{\lambda D}{2d}\]
(b) \[\frac{\lambda D}{d}\]
(c) \[\frac{\lambda D}{4d}\]
Answer the following question.
In the diffraction due to a single slit experiment, the aperture of the slit is 3 mm. If monochromatic light of wavelength 620 nm is incident normally on the slit, calculate the separation between the first order minima and the 3rd order maxima on one side of the screen. The distance between the slit and the screen is 1.5 m.
(a) Can the interference pattern be produced by two independent monochromatic sources of light? Explain.
(b) The intensity at the central maximum (O) in Young's double-slit experimental set-up shown in the figure is IO. If the distance OP equals one-third of the fringe width of the pattern, show that the intensity at point P, would `"I"_°/4`
(c) In Young's double-slit experiment, the slits are separated by 0⋅5 mm and the screen is placed 1⋅0 m away from the slit. It is found that the 5th bright fringe is at a distance of 4⋅13 mm from the 2nd dark fringe. Find the wavelength of light used.
Using the monochromatic light of the wavelength in the experimental set-up of the diffraction pattern as well as in the interference pattern where the slit separation is 1 mm, 10 interference fringes are found to be within the central maximum of the diffraction pattern. Determine the width of the single slit, if the screen is kept at the same distance from the slit in the two cases.
A narrow slit is illuminated by a parallel beam of monochromatic light of wavelength λ equal to 6000 Å and the angular width of the central maximum in the resulting diffraction pattern is measured. When the slit is next illuminated by light of wavelength λ’, the angular width decreases by 30%. Calculate the value of the wavelength λ’.
