In Young’s double-slit experiment show that β = λ D d where the terms have their usual meanings.

Young’s double slit experiment demonstrated the phenomenon of interference of light. Consider two fine slits S 1 a n d S 2 at a small distance d apart. Let the slits be illuminated by a monochromatic source of light of wavelength l Let G G ' be a screen kept at a distance D from the slits. The two waves emanating from slits S 1 a n d S 2 superimpose on each other resulting in the formation of an interference pattern on the screen placed parallel to the slits. Let O be the centre of the distance between the slits. The intensity of light at a point on the screen will depend on the path difference between the two waves reaching that point. Consider an arbitrary point P at a distance x from O on the screen. Path difference between two waves at P = S 2 P - S 1 P On the screen, the intensity at point P is maximum or minimum as the path difference from the two slits is an integral multiple of wave length of an odd multiple of half-wave length For maxima S 1 P 2 - S 2 P 2 = D 2 + x + d 2 2 - D 2 + x - d 2 2 = 2 x d S 2 P - S 1 P = 2 xd S 2 P + S 1 P as d < < < D S 2 P + S 1 P = 2 D ( S 2 P = S 1 P = d ) S 2 P - S 1 P = xd D So, for maxima xd D = nλ or x = nλ d . D For minima xd D = ( n + 1 ) 2 λ The fringe width is the distance between two consecutive bright and dark fingers β = x n + 1 - x n = n + 1 λD d - nλD d = λ D d .

Draw a neat labelled diagram of Young’s double-slit experiment. Show that β = λ a , where the terms have their usual meaning (either for bright or dark fringe)

Young’s double slit experiment demonstrated the phenomenon of interference of light. Consider two fine slits S 1 a n d S 2 at a small distance d apart. Let the slits be illuminated by a monochromatic source of light of wavelength l Let G G ' be a screen kept at a distance D from the slits. The two waves emanating from slits S 1 a n d S 2 superimpose on each other resulting in the formation of an interference pattern on the screen placed parallel to the slits. Let O be the centre of the distance between the slits. The intensity of light at a point on the screen will depend on the path difference between the two waves reaching that point. Consider an arbitrary point P at a distance x from O on the screen. Path difference between two waves at P = S 2 P - S 1 P On the screen, the intensity at point P is maximum or minimum as the path difference from the two slits is an integral multiple of wave length of an odd multiple of half-wave length For maxima S 1 P 2 - S 2 P 2 = D 2 + x + d 2 2 - D 2 + x - d 2 2 = 2 x d S 2 P - S 1 P = 2 xd S 2 P + S 1 P as d < < < D S 2 P + S 1 P = 2 D ( S 2 P = S 1 P = d ) S 2 P - S 1 P = xd D So, for maxima xd D = nλ or x = nλ d . D For minima xd D = ( n + 1 ) 2 λ The fringe width is the distance between two consecutive bright and dark fingers β = x n + 1 - x n = n + 1 λD d - nλD d = λ D d . This is the required equation.

E M B I B E

ISC Physics Class 12, Part-2>Chapter 7 - Interference of Light>QUESTIONS>Q 2

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What are coherent sources?

Important Questions on Interference of Light

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ISC Physics Class 12, Part-2>Chapter 7 - Interference of Light>QUESTIONS>Q 2

In Young’s double-slit experiment, what is the path difference between the two light waves, forming the $5^{th}$ bright band (fringe) on the screen?

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ISC Physics Class 12, Part-2>Chapter 7 - Interference of Light>QUESTIONS>Q 3

Describe an expression for the fringe-width in Young’s double-slit experiment. Use $λ$ as the wavelength of the monochromatic source, $D$ as the distance of the screen from the slits and $d$ as the separation between the slits.

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ISC Physics Class 12, Part-2>Chapter 7 - Interference of Light>QUESTIONS>Q 4

In Young’s double-slit experiment, what is meant by fringe-width or fringe separation? State two ways of increasing the fringe-width, without changing the source of light.

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ISC Physics Class 12, Part-2>Chapter 7 - Interference of Light>QUESTIONS>Q 5

In Young’s double-slit experiment show that

β = \frac{λ D}{d}

where the terms have their usual meanings.

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ISC Physics Class 12, Part-2>Chapter 7 - Interference of Light>QUESTIONS>Q 6

Draw a neat labelled diagram of Young’s double-slit experiment. Show that $β = \frac{λ}{a}$ , where the terms have their usual meaning (either for bright or dark fringe)

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ISC Physics Class 12, Part-2>Chapter 7 - Interference of Light>QUESTIONS>Q 7

In Young’s double-slit experiment show graphically how intensity of light varies with distance.

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ISC Physics Class 12, Part-2>Chapter 7 - Interference of Light>QUESTIONS>Q 1

What is interference of light? Name the interference happen at a place where intensity of light is maximum and minimum. Write four conditions to sustain interference.

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ISC Physics Class 12, Part-2>Chapter 7 - Interference of Light>QUESTIONS>Q 2

Write the relation between phase difference and path difference for two interfering light rays. If path difference between two waves is whole multiple of wavelength, find the corresponding path difference. Define visible/contrast interference.

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