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प्रश्न
In a double slit interference experiment, the separation between the slits is 1.0 mm, the wavelength of light used is 5.0 × 10−7 m and the distance of the screen from the slits is 1.0m. (a) Find the distance of the centre of the first minimum from the centre of the central maximum. (b) How many bright fringes are formed in one centimetre width on the screen?
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उत्तर
Given
Separation between the two slits,
\[d = 1 mm = {10}^{- 3} m\]
Wavelength of the light used,
\[\lambda = 5 . 0 \times {10}^{- 7} m\]
Distance between screen and slit,
\[D = 1 m\]
(a) The distance of the centre of the first minimum from the centre of the central maximum, \[x = \frac{\text{width of central maxima}}{2}\]
That is,
\[x = \frac{\beta}{2} = \frac{\lambda D}{2d}...........(1)\]
\[= \frac{5 \times {10}^{- 7} \times 1}{2 \times {10}^{- 3}}\]
\[ = 2 . 5 \times {10}^{- 4} m = 0 . 25 mm\]
(b) From equation (1),
fringe width,
\[\beta = 2 \times x = 0 . 50 mm\]
So, number of bright fringes formed in one centimetre (10 mm) = \[\frac{10}{0 . 50} = 20\]
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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.
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Derive an expression for path difference in Young’s double slit experiment and obtain the conditions for constructive and destructive interference at a point on the screen.
What is the effect on the fringe width if the distance between the slits is reduced keeping other parameters same?
Explain two features to distinguish between the interference pattern in Young's double slit experiment with the diffraction pattern obtained due to a single slit.
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What is the effect on the interference fringes to a Young’s double slit experiment when
(i) the separation between the two slits is decreased?
(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.
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