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 4

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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.

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

Describe Young’s double-slit experiment and show that width of bright fringe is equal to width of dark fringe.

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

Obtain an expression for path difference i.e., $P.D. = \frac{xd}{D}$ where $d$ is the distance between two sources, $D$ is the distance of the screen from the slit and $x$ is the distance of the interfering point from the centre of the screen.

If Young’s double-slit experiment set up is immersed in water, what would happen to the width of the fringe?

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

Define coherent sources and monochromatic light. Name a light which can be considered as monochromatic. Write three values of path difference and corresponding values of phase difference for destructive interference.

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