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9 | 1339-1342 | Young worked
on a wide variety of
scientific problems, ranging
from the structure of the eye
and the mechanism of
vision to the decipherment
of the Rosetta stone He
revived the wave theory of
light and recognised that
interference phenomena
provide proof of the wave
properties of light THOMAS YOUNG (1773 – 1829)
We will have constructive interference resulting in a bright
region when xd
D
= nl That is,
x = xn = n D
λd
; n = 0, ± 1, ± 2, |
9 | 1340-1343 | He
revived the wave theory of
light and recognised that
interference phenomena
provide proof of the wave
properties of light THOMAS YOUNG (1773 – 1829)
We will have constructive interference resulting in a bright
region when xd
D
= nl That is,
x = xn = n D
λd
; n = 0, ± 1, ± 2, (10 |
9 | 1341-1344 | THOMAS YOUNG (1773 – 1829)
We will have constructive interference resulting in a bright
region when xd
D
= nl That is,
x = xn = n D
λd
; n = 0, ± 1, ± 2, (10 13)
On the other hand, we will have destructive
interference resulting in a dark region when xd
D
= (n+
1
2 ) l
that is
x = xn = (n+
1
2 )
;
0, 1,
2
D
n
d
(10 |
9 | 1342-1345 | That is,
x = xn = n D
λd
; n = 0, ± 1, ± 2, (10 13)
On the other hand, we will have destructive
interference resulting in a dark region when xd
D
= (n+
1
2 ) l
that is
x = xn = (n+
1
2 )
;
0, 1,
2
D
n
d
(10 14)
Thus dark and bright bands appear on the screen,
as shown in Fig |
9 | 1343-1346 | (10 13)
On the other hand, we will have destructive
interference resulting in a dark region when xd
D
= (n+
1
2 ) l
that is
x = xn = (n+
1
2 )
;
0, 1,
2
D
n
d
(10 14)
Thus dark and bright bands appear on the screen,
as shown in Fig 10 |
9 | 1344-1347 | 13)
On the other hand, we will have destructive
interference resulting in a dark region when xd
D
= (n+
1
2 ) l
that is
x = xn = (n+
1
2 )
;
0, 1,
2
D
n
d
(10 14)
Thus dark and bright bands appear on the screen,
as shown in Fig 10 13 |
9 | 1345-1348 | 14)
Thus dark and bright bands appear on the screen,
as shown in Fig 10 13 Such bands are called fringes |
9 | 1346-1349 | 10 13 Such bands are called fringes Equations (10 |
9 | 1347-1350 | 13 Such bands are called fringes Equations (10 13) and (10 |
9 | 1348-1351 | Such bands are called fringes Equations (10 13) and (10 14) show that dark and
bright fringes are equally spaced |
9 | 1349-1352 | Equations (10 13) and (10 14) show that dark and
bright fringes are equally spaced 10 |
9 | 1350-1353 | 13) and (10 14) show that dark and
bright fringes are equally spaced 10 6 DIFFRACTION
If we look clearly at the shadow cast by an opaque object, close to the
region of geometrical shadow, there are alternate dark and bright regions
just like in interference |
9 | 1351-1354 | 14) show that dark and
bright fringes are equally spaced 10 6 DIFFRACTION
If we look clearly at the shadow cast by an opaque object, close to the
region of geometrical shadow, there are alternate dark and bright regions
just like in interference This happens due to the phenomenon of
diffraction |
9 | 1352-1355 | 10 6 DIFFRACTION
If we look clearly at the shadow cast by an opaque object, close to the
region of geometrical shadow, there are alternate dark and bright regions
just like in interference This happens due to the phenomenon of
diffraction Diffraction is a general characteristic exhibited by all types of
waves, be it sound waves, light waves, water waves or matter waves |
9 | 1353-1356 | 6 DIFFRACTION
If we look clearly at the shadow cast by an opaque object, close to the
region of geometrical shadow, there are alternate dark and bright regions
just like in interference This happens due to the phenomenon of
diffraction Diffraction is a general characteristic exhibited by all types of
waves, be it sound waves, light waves, water waves or matter waves Since
the wavelength of light is much smaller than the dimensions of most
obstacles; we do not encounter diffraction effects of light in everyday
Rationalised 2023-24
267
Wave Optics
observations |
9 | 1354-1357 | This happens due to the phenomenon of
diffraction Diffraction is a general characteristic exhibited by all types of
waves, be it sound waves, light waves, water waves or matter waves Since
the wavelength of light is much smaller than the dimensions of most
obstacles; we do not encounter diffraction effects of light in everyday
Rationalised 2023-24
267
Wave Optics
observations However, the finite resolution of our eye or of optical
instruments such as telescopes or microscopes is limited due to the
phenomenon of diffraction |
9 | 1355-1358 | Diffraction is a general characteristic exhibited by all types of
waves, be it sound waves, light waves, water waves or matter waves Since
the wavelength of light is much smaller than the dimensions of most
obstacles; we do not encounter diffraction effects of light in everyday
Rationalised 2023-24
267
Wave Optics
observations However, the finite resolution of our eye or of optical
instruments such as telescopes or microscopes is limited due to the
phenomenon of diffraction Indeed the colours that you see when a CD is
viewed is due to diffraction effects |
9 | 1356-1359 | Since
the wavelength of light is much smaller than the dimensions of most
obstacles; we do not encounter diffraction effects of light in everyday
Rationalised 2023-24
267
Wave Optics
observations However, the finite resolution of our eye or of optical
instruments such as telescopes or microscopes is limited due to the
phenomenon of diffraction Indeed the colours that you see when a CD is
viewed is due to diffraction effects We will now discuss the phenomenon
of diffraction |
9 | 1357-1360 | However, the finite resolution of our eye or of optical
instruments such as telescopes or microscopes is limited due to the
phenomenon of diffraction Indeed the colours that you see when a CD is
viewed is due to diffraction effects We will now discuss the phenomenon
of diffraction 10 |
9 | 1358-1361 | Indeed the colours that you see when a CD is
viewed is due to diffraction effects We will now discuss the phenomenon
of diffraction 10 6 |
9 | 1359-1362 | We will now discuss the phenomenon
of diffraction 10 6 1 The single slit
In the discussion of Young’s experiment, we stated that a single narrow
slit acts as a new source from which light spreads out |
9 | 1360-1363 | 10 6 1 The single slit
In the discussion of Young’s experiment, we stated that a single narrow
slit acts as a new source from which light spreads out Even before Young,
early experimenters – including Newton – had noticed that light spreads
out from narrow holes and slits |
9 | 1361-1364 | 6 1 The single slit
In the discussion of Young’s experiment, we stated that a single narrow
slit acts as a new source from which light spreads out Even before Young,
early experimenters – including Newton – had noticed that light spreads
out from narrow holes and slits It seems to turn around corners and
enter regions where we would expect a shadow |
9 | 1362-1365 | 1 The single slit
In the discussion of Young’s experiment, we stated that a single narrow
slit acts as a new source from which light spreads out Even before Young,
early experimenters – including Newton – had noticed that light spreads
out from narrow holes and slits It seems to turn around corners and
enter regions where we would expect a shadow These effects, known as
diffraction, can only be properly understood using wave ideas |
9 | 1363-1366 | Even before Young,
early experimenters – including Newton – had noticed that light spreads
out from narrow holes and slits It seems to turn around corners and
enter regions where we would expect a shadow These effects, known as
diffraction, can only be properly understood using wave ideas After all,
you are hardly surprised to hear sound
waves from someone talking around a corner |
9 | 1364-1367 | It seems to turn around corners and
enter regions where we would expect a shadow These effects, known as
diffraction, can only be properly understood using wave ideas After all,
you are hardly surprised to hear sound
waves from someone talking around a corner When the double slit in Young’s
experiment is replaced by a single narrow
slit (illuminated by a monochromatic
source), a broad pattern with a central bright
region is seen |
9 | 1365-1368 | These effects, known as
diffraction, can only be properly understood using wave ideas After all,
you are hardly surprised to hear sound
waves from someone talking around a corner When the double slit in Young’s
experiment is replaced by a single narrow
slit (illuminated by a monochromatic
source), a broad pattern with a central bright
region is seen On both sides, there are
alternate dark and bright regions, the
intensity becoming weaker away from the
centre (Fig |
9 | 1366-1369 | After all,
you are hardly surprised to hear sound
waves from someone talking around a corner When the double slit in Young’s
experiment is replaced by a single narrow
slit (illuminated by a monochromatic
source), a broad pattern with a central bright
region is seen On both sides, there are
alternate dark and bright regions, the
intensity becoming weaker away from the
centre (Fig 10 |
9 | 1367-1370 | When the double slit in Young’s
experiment is replaced by a single narrow
slit (illuminated by a monochromatic
source), a broad pattern with a central bright
region is seen On both sides, there are
alternate dark and bright regions, the
intensity becoming weaker away from the
centre (Fig 10 15) |
9 | 1368-1371 | On both sides, there are
alternate dark and bright regions, the
intensity becoming weaker away from the
centre (Fig 10 15) To understand this, go
to Fig |
9 | 1369-1372 | 10 15) To understand this, go
to Fig 10 |
9 | 1370-1373 | 15) To understand this, go
to Fig 10 14, which shows a parallel beam
of light falling normally on a single slit LN of
width a |
9 | 1371-1374 | To understand this, go
to Fig 10 14, which shows a parallel beam
of light falling normally on a single slit LN of
width a The diffracted light goes on to meet
a screen |
9 | 1372-1375 | 10 14, which shows a parallel beam
of light falling normally on a single slit LN of
width a The diffracted light goes on to meet
a screen The midpoint of the slit is M |
9 | 1373-1376 | 14, which shows a parallel beam
of light falling normally on a single slit LN of
width a The diffracted light goes on to meet
a screen The midpoint of the slit is M A straight line through M perpendicular
to the slit plane meets the screen at C |
9 | 1374-1377 | The diffracted light goes on to meet
a screen The midpoint of the slit is M A straight line through M perpendicular
to the slit plane meets the screen at C We want the
intensity at any point P on the screen |
9 | 1375-1378 | The midpoint of the slit is M A straight line through M perpendicular
to the slit plane meets the screen at C We want the
intensity at any point P on the screen As before, straight
lines joining P to the different points L,M,N, etc |
9 | 1376-1379 | A straight line through M perpendicular
to the slit plane meets the screen at C We want the
intensity at any point P on the screen As before, straight
lines joining P to the different points L,M,N, etc , can be
treated as parallel, making an angle q with the
normal MC |
9 | 1377-1380 | We want the
intensity at any point P on the screen As before, straight
lines joining P to the different points L,M,N, etc , can be
treated as parallel, making an angle q with the
normal MC The basic idea is to divide the slit into much smaller
parts, and add their contributions at P with the proper
phase differences |
9 | 1378-1381 | As before, straight
lines joining P to the different points L,M,N, etc , can be
treated as parallel, making an angle q with the
normal MC The basic idea is to divide the slit into much smaller
parts, and add their contributions at P with the proper
phase differences We are treating different parts of the
wavefront at the slit as secondary sources |
9 | 1379-1382 | , can be
treated as parallel, making an angle q with the
normal MC The basic idea is to divide the slit into much smaller
parts, and add their contributions at P with the proper
phase differences We are treating different parts of the
wavefront at the slit as secondary sources Because the
incoming wavefront is parallel to the plane of the slit, these
sources are in phase |
9 | 1380-1383 | The basic idea is to divide the slit into much smaller
parts, and add their contributions at P with the proper
phase differences We are treating different parts of the
wavefront at the slit as secondary sources Because the
incoming wavefront is parallel to the plane of the slit, these
sources are in phase It is observed that the intensity has a central
maximum at q = 0 and other secondary maxima at q l
(n+1/2) l/a, which go on becoming weaker and weaker
with increasing n |
9 | 1381-1384 | We are treating different parts of the
wavefront at the slit as secondary sources Because the
incoming wavefront is parallel to the plane of the slit, these
sources are in phase It is observed that the intensity has a central
maximum at q = 0 and other secondary maxima at q l
(n+1/2) l/a, which go on becoming weaker and weaker
with increasing n The minima (zero intensity) are at q l
nl/a, n = ±1, ±2, ±3, |
9 | 1382-1385 | Because the
incoming wavefront is parallel to the plane of the slit, these
sources are in phase It is observed that the intensity has a central
maximum at q = 0 and other secondary maxima at q l
(n+1/2) l/a, which go on becoming weaker and weaker
with increasing n The minima (zero intensity) are at q l
nl/a, n = ±1, ±2, ±3, The photograph and intensity pattern corresponding
to it is shown in Fig |
9 | 1383-1386 | It is observed that the intensity has a central
maximum at q = 0 and other secondary maxima at q l
(n+1/2) l/a, which go on becoming weaker and weaker
with increasing n The minima (zero intensity) are at q l
nl/a, n = ±1, ±2, ±3, The photograph and intensity pattern corresponding
to it is shown in Fig 10 |
9 | 1384-1387 | The minima (zero intensity) are at q l
nl/a, n = ±1, ±2, ±3, The photograph and intensity pattern corresponding
to it is shown in Fig 10 15 |
9 | 1385-1388 | The photograph and intensity pattern corresponding
to it is shown in Fig 10 15 There has been prolonged discussion about
difference between intereference and diffraction among
FIGURE 10 |
9 | 1386-1389 | 10 15 There has been prolonged discussion about
difference between intereference and diffraction among
FIGURE 10 14 The geometry of path
differences for diffraction by a single slit |
9 | 1387-1390 | 15 There has been prolonged discussion about
difference between intereference and diffraction among
FIGURE 10 14 The geometry of path
differences for diffraction by a single slit FIGURE 10 |
9 | 1388-1391 | There has been prolonged discussion about
difference between intereference and diffraction among
FIGURE 10 14 The geometry of path
differences for diffraction by a single slit FIGURE 10 15 Intensity
distribution and photograph of
fringes due to diffraction
at single slit |
9 | 1389-1392 | 14 The geometry of path
differences for diffraction by a single slit FIGURE 10 15 Intensity
distribution and photograph of
fringes due to diffraction
at single slit Rationalised 2023-24
Physics
268
FIGURE 10 |
9 | 1390-1393 | FIGURE 10 15 Intensity
distribution and photograph of
fringes due to diffraction
at single slit Rationalised 2023-24
Physics
268
FIGURE 10 16
Holding two blades to
form a single slit |
9 | 1391-1394 | 15 Intensity
distribution and photograph of
fringes due to diffraction
at single slit Rationalised 2023-24
Physics
268
FIGURE 10 16
Holding two blades to
form a single slit A
bulb filament viewed
through this shows
clear diffraction
bands |
9 | 1392-1395 | Rationalised 2023-24
Physics
268
FIGURE 10 16
Holding two blades to
form a single slit A
bulb filament viewed
through this shows
clear diffraction
bands scientists since the discovery of these phenomena |
9 | 1393-1396 | 16
Holding two blades to
form a single slit A
bulb filament viewed
through this shows
clear diffraction
bands scientists since the discovery of these phenomena In this context, it is
interesting to note what Richard Feynman* has said in his famous
Feynman Lectures on Physics:
No one has ever been able to define the difference between
interference and diffraction satisfactorily |
9 | 1394-1397 | A
bulb filament viewed
through this shows
clear diffraction
bands scientists since the discovery of these phenomena In this context, it is
interesting to note what Richard Feynman* has said in his famous
Feynman Lectures on Physics:
No one has ever been able to define the difference between
interference and diffraction satisfactorily It is just a question
of usage, and there is no specific, important physical difference
between them |
9 | 1395-1398 | scientists since the discovery of these phenomena In this context, it is
interesting to note what Richard Feynman* has said in his famous
Feynman Lectures on Physics:
No one has ever been able to define the difference between
interference and diffraction satisfactorily It is just a question
of usage, and there is no specific, important physical difference
between them The best we can do is, roughly speaking, is to
say that when there are only a few sources, say two interfering
sources, then the result is usually called interference, but if there
is a large number of them, it seems that the word diffraction is
more often used |
9 | 1396-1399 | In this context, it is
interesting to note what Richard Feynman* has said in his famous
Feynman Lectures on Physics:
No one has ever been able to define the difference between
interference and diffraction satisfactorily It is just a question
of usage, and there is no specific, important physical difference
between them The best we can do is, roughly speaking, is to
say that when there are only a few sources, say two interfering
sources, then the result is usually called interference, but if there
is a large number of them, it seems that the word diffraction is
more often used In the double-slit experiment, we must note that the pattern on the
screen is actually a superposition of single-slit diffraction from each slit
or hole, and the double-slit interference pattern |
9 | 1397-1400 | It is just a question
of usage, and there is no specific, important physical difference
between them The best we can do is, roughly speaking, is to
say that when there are only a few sources, say two interfering
sources, then the result is usually called interference, but if there
is a large number of them, it seems that the word diffraction is
more often used In the double-slit experiment, we must note that the pattern on the
screen is actually a superposition of single-slit diffraction from each slit
or hole, and the double-slit interference pattern 10 |
9 | 1398-1401 | The best we can do is, roughly speaking, is to
say that when there are only a few sources, say two interfering
sources, then the result is usually called interference, but if there
is a large number of them, it seems that the word diffraction is
more often used In the double-slit experiment, we must note that the pattern on the
screen is actually a superposition of single-slit diffraction from each slit
or hole, and the double-slit interference pattern 10 6 |
9 | 1399-1402 | In the double-slit experiment, we must note that the pattern on the
screen is actually a superposition of single-slit diffraction from each slit
or hole, and the double-slit interference pattern 10 6 2 Seeing the single slit diffraction pattern
It is surprisingly easy to see the single-slit diffraction pattern for oneself |
9 | 1400-1403 | 10 6 2 Seeing the single slit diffraction pattern
It is surprisingly easy to see the single-slit diffraction pattern for oneself The equipment needed can be found in most homes –– two razor blades
and one clear glass electric bulb preferably with a straight filament |
9 | 1401-1404 | 6 2 Seeing the single slit diffraction pattern
It is surprisingly easy to see the single-slit diffraction pattern for oneself The equipment needed can be found in most homes –– two razor blades
and one clear glass electric bulb preferably with a straight filament One
has to hold the two blades so that the edges are parallel and have a
narrow slit in between |
9 | 1402-1405 | 2 Seeing the single slit diffraction pattern
It is surprisingly easy to see the single-slit diffraction pattern for oneself The equipment needed can be found in most homes –– two razor blades
and one clear glass electric bulb preferably with a straight filament One
has to hold the two blades so that the edges are parallel and have a
narrow slit in between This is easily done with the thumb and forefingers
(Fig |
9 | 1403-1406 | The equipment needed can be found in most homes –– two razor blades
and one clear glass electric bulb preferably with a straight filament One
has to hold the two blades so that the edges are parallel and have a
narrow slit in between This is easily done with the thumb and forefingers
(Fig 10 |
9 | 1404-1407 | One
has to hold the two blades so that the edges are parallel and have a
narrow slit in between This is easily done with the thumb and forefingers
(Fig 10 16) |
9 | 1405-1408 | This is easily done with the thumb and forefingers
(Fig 10 16) Keep the slit parallel to the filament, right in front of the eye |
9 | 1406-1409 | 10 16) Keep the slit parallel to the filament, right in front of the eye Use
spectacles if you normally do |
9 | 1407-1410 | 16) Keep the slit parallel to the filament, right in front of the eye Use
spectacles if you normally do With slight adjustment of the width of
the slit and the parallelism of the edges, the pattern should be seen
with its bright and dark bands |
9 | 1408-1411 | Keep the slit parallel to the filament, right in front of the eye Use
spectacles if you normally do With slight adjustment of the width of
the slit and the parallelism of the edges, the pattern should be seen
with its bright and dark bands Since the position of all the bands
(except the central one) depends on wavelength, they will show some
colours |
9 | 1409-1412 | Use
spectacles if you normally do With slight adjustment of the width of
the slit and the parallelism of the edges, the pattern should be seen
with its bright and dark bands Since the position of all the bands
(except the central one) depends on wavelength, they will show some
colours Using a filter for red or blue will make the fringes clearer |
9 | 1410-1413 | With slight adjustment of the width of
the slit and the parallelism of the edges, the pattern should be seen
with its bright and dark bands Since the position of all the bands
(except the central one) depends on wavelength, they will show some
colours Using a filter for red or blue will make the fringes clearer With both filters available, the wider fringes for red compared to blue
can be seen |
9 | 1411-1414 | Since the position of all the bands
(except the central one) depends on wavelength, they will show some
colours Using a filter for red or blue will make the fringes clearer With both filters available, the wider fringes for red compared to blue
can be seen In this experiment, the filament plays the role of the first slit S in
Fig |
9 | 1412-1415 | Using a filter for red or blue will make the fringes clearer With both filters available, the wider fringes for red compared to blue
can be seen In this experiment, the filament plays the role of the first slit S in
Fig 10 |
9 | 1413-1416 | With both filters available, the wider fringes for red compared to blue
can be seen In this experiment, the filament plays the role of the first slit S in
Fig 10 15 |
9 | 1414-1417 | In this experiment, the filament plays the role of the first slit S in
Fig 10 15 The lens of the eye focuses the pattern on the screen (the
retina of the eye) |
9 | 1415-1418 | 10 15 The lens of the eye focuses the pattern on the screen (the
retina of the eye) With some effort, one can cut a double slit in an aluminium foil with
a blade |
9 | 1416-1419 | 15 The lens of the eye focuses the pattern on the screen (the
retina of the eye) With some effort, one can cut a double slit in an aluminium foil with
a blade The bulb filament can be viewed as before to repeat Young’s
experiment |
9 | 1417-1420 | The lens of the eye focuses the pattern on the screen (the
retina of the eye) With some effort, one can cut a double slit in an aluminium foil with
a blade The bulb filament can be viewed as before to repeat Young’s
experiment In daytime, there is another suitable bright source subtending
a small angle at the eye |
9 | 1418-1421 | With some effort, one can cut a double slit in an aluminium foil with
a blade The bulb filament can be viewed as before to repeat Young’s
experiment In daytime, there is another suitable bright source subtending
a small angle at the eye This is the reflection of the Sun in any shiny
convex surface (e |
9 | 1419-1422 | The bulb filament can be viewed as before to repeat Young’s
experiment In daytime, there is another suitable bright source subtending
a small angle at the eye This is the reflection of the Sun in any shiny
convex surface (e g |
9 | 1420-1423 | In daytime, there is another suitable bright source subtending
a small angle at the eye This is the reflection of the Sun in any shiny
convex surface (e g , a cycle bell) |
9 | 1421-1424 | This is the reflection of the Sun in any shiny
convex surface (e g , a cycle bell) Do not try direct sunlight – it can damage
the eye and will not give fringes anyway as the Sun subtends an angle
of (1/2)° |
9 | 1422-1425 | g , a cycle bell) Do not try direct sunlight – it can damage
the eye and will not give fringes anyway as the Sun subtends an angle
of (1/2)° In interference and diffraction, light energy is redistributed |
9 | 1423-1426 | , a cycle bell) Do not try direct sunlight – it can damage
the eye and will not give fringes anyway as the Sun subtends an angle
of (1/2)° In interference and diffraction, light energy is redistributed If it
reduces in one region, producing a dark fringe, it increases in another
region, producing a bright fringe |
9 | 1424-1427 | Do not try direct sunlight – it can damage
the eye and will not give fringes anyway as the Sun subtends an angle
of (1/2)° In interference and diffraction, light energy is redistributed If it
reduces in one region, producing a dark fringe, it increases in another
region, producing a bright fringe There is no gain or loss of energy,
which is consistent with the principle of conservation of energy |
9 | 1425-1428 | In interference and diffraction, light energy is redistributed If it
reduces in one region, producing a dark fringe, it increases in another
region, producing a bright fringe There is no gain or loss of energy,
which is consistent with the principle of conservation of energy *
Richand Feynman was one of the recipients of the 1965 Nobel Prize in Physics
for his fundamental work in quantum electrodynamics |
9 | 1426-1429 | If it
reduces in one region, producing a dark fringe, it increases in another
region, producing a bright fringe There is no gain or loss of energy,
which is consistent with the principle of conservation of energy *
Richand Feynman was one of the recipients of the 1965 Nobel Prize in Physics
for his fundamental work in quantum electrodynamics Rationalised 2023-24
269
Wave Optics
10 |
9 | 1427-1430 | There is no gain or loss of energy,
which is consistent with the principle of conservation of energy *
Richand Feynman was one of the recipients of the 1965 Nobel Prize in Physics
for his fundamental work in quantum electrodynamics Rationalised 2023-24
269
Wave Optics
10 7 POLARISATION
Consider holding a long string that is held horizontally, the other end of
which is assumed to be fixed |
9 | 1428-1431 | *
Richand Feynman was one of the recipients of the 1965 Nobel Prize in Physics
for his fundamental work in quantum electrodynamics Rationalised 2023-24
269
Wave Optics
10 7 POLARISATION
Consider holding a long string that is held horizontally, the other end of
which is assumed to be fixed If we move the end of the string up and
down in a periodic manner, we will generate a wave propagating in the
+x direction (Fig |
9 | 1429-1432 | Rationalised 2023-24
269
Wave Optics
10 7 POLARISATION
Consider holding a long string that is held horizontally, the other end of
which is assumed to be fixed If we move the end of the string up and
down in a periodic manner, we will generate a wave propagating in the
+x direction (Fig 10 |
9 | 1430-1433 | 7 POLARISATION
Consider holding a long string that is held horizontally, the other end of
which is assumed to be fixed If we move the end of the string up and
down in a periodic manner, we will generate a wave propagating in the
+x direction (Fig 10 17) |
9 | 1431-1434 | If we move the end of the string up and
down in a periodic manner, we will generate a wave propagating in the
+x direction (Fig 10 17) Such a wave could be described by the following
equation
FIGURE 10 |
9 | 1432-1435 | 10 17) Such a wave could be described by the following
equation
FIGURE 10 17 (a) The curves represent the displacement of a string at
t = 0 and at t = Dt, respectively when a sinusoidal wave is propagating
in the +x-direction |
9 | 1433-1436 | 17) Such a wave could be described by the following
equation
FIGURE 10 17 (a) The curves represent the displacement of a string at
t = 0 and at t = Dt, respectively when a sinusoidal wave is propagating
in the +x-direction (b) The curve represents the time variation
of the displacement at x = 0 when a sinusoidal wave is propagating
in the +x-direction |
9 | 1434-1437 | Such a wave could be described by the following
equation
FIGURE 10 17 (a) The curves represent the displacement of a string at
t = 0 and at t = Dt, respectively when a sinusoidal wave is propagating
in the +x-direction (b) The curve represents the time variation
of the displacement at x = 0 when a sinusoidal wave is propagating
in the +x-direction At x = Dx, the time variation of the
displacement will be slightly displaced to the right |
9 | 1435-1438 | 17 (a) The curves represent the displacement of a string at
t = 0 and at t = Dt, respectively when a sinusoidal wave is propagating
in the +x-direction (b) The curve represents the time variation
of the displacement at x = 0 when a sinusoidal wave is propagating
in the +x-direction At x = Dx, the time variation of the
displacement will be slightly displaced to the right y (x,t) = a sin (kx – wt)
(10 |
9 | 1436-1439 | (b) The curve represents the time variation
of the displacement at x = 0 when a sinusoidal wave is propagating
in the +x-direction At x = Dx, the time variation of the
displacement will be slightly displaced to the right y (x,t) = a sin (kx – wt)
(10 15)
where a and w (= 2pn) represent the amplitude and the angular frequency
of the wave, respectively; further,
2
k
λ
π
=
(10 |
9 | 1437-1440 | At x = Dx, the time variation of the
displacement will be slightly displaced to the right y (x,t) = a sin (kx – wt)
(10 15)
where a and w (= 2pn) represent the amplitude and the angular frequency
of the wave, respectively; further,
2
k
λ
π
=
(10 16)
represents the wavelength associated with the wave |
9 | 1438-1441 | y (x,t) = a sin (kx – wt)
(10 15)
where a and w (= 2pn) represent the amplitude and the angular frequency
of the wave, respectively; further,
2
k
λ
π
=
(10 16)
represents the wavelength associated with the wave We had discussed
propagation of such waves in Chapter 14 of Class XI textbook |
Subsets and Splits