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 20

HARD

12th ICSE

IMPORTANT

Earn 100

Find the maximum intensity in the interference pattern of Young’s double-slit compared to the intensity due to one slit only.

Important Questions on Interference of Light

HARD

12th ICSE

IMPORTANT

ISC Physics Class 12, Part-2>Chapter 7 - Interference of Light>QUESTIONS>Q 21

How will the interference pattern of Young’s double-slit change, if one of the two slits is covered by a paper which transmits only half of the light intensity?

HARD

12th ICSE

IMPORTANT

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

What do you mean by interference of light? State and explain the conditions under which light from two sources can interfere.

MEDIUM

12th ICSE

IMPORTANT

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

What are coherent sources?

MEDIUM

12th ICSE

IMPORTANT

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?

MEDIUM

12th ICSE

IMPORTANT

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.

MEDIUM

12th ICSE

IMPORTANT

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.

HARD

12th ICSE

IMPORTANT

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.

HARD

12th ICSE

IMPORTANT

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)

Learn and Prepare for any exam you want !

|

|

|

|

|

|

|

|