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9 | 1139-1142 | Let CE represent a tangent plane
drawn from the point C on to the sphere Then, AE = v2 t
and CE would represent the refracted wavefront If we
now consider the triangles ABC and AEC, we readily
obtain
sin i =
1
BC
AC
AC
=v τ
(10 1)
and
sin r =
2
AE
AC
AC
=v τ
(10 |
9 | 1140-1143 | Then, AE = v2 t
and CE would represent the refracted wavefront If we
now consider the triangles ABC and AEC, we readily
obtain
sin i =
1
BC
AC
AC
=v τ
(10 1)
and
sin r =
2
AE
AC
AC
=v τ
(10 2)
where i and r are the angles of incidence and refraction,
respectively |
9 | 1141-1144 | If we
now consider the triangles ABC and AEC, we readily
obtain
sin i =
1
BC
AC
AC
=v τ
(10 1)
and
sin r =
2
AE
AC
AC
=v τ
(10 2)
where i and r are the angles of incidence and refraction,
respectively Thus we obtain
1
2
sin
sin
i
v
r
=v
(10 |
9 | 1142-1145 | 1)
and
sin r =
2
AE
AC
AC
=v τ
(10 2)
where i and r are the angles of incidence and refraction,
respectively Thus we obtain
1
2
sin
sin
i
v
r
=v
(10 3)
From the above equation, we get the important result
that if r < i (i |
9 | 1143-1146 | 2)
where i and r are the angles of incidence and refraction,
respectively Thus we obtain
1
2
sin
sin
i
v
r
=v
(10 3)
From the above equation, we get the important result
that if r < i (i e |
9 | 1144-1147 | Thus we obtain
1
2
sin
sin
i
v
r
=v
(10 3)
From the above equation, we get the important result
that if r < i (i e , if the ray bends toward the normal), the
speed of the light wave in the second medium (v2) will be
less then the speed of the light wave in the first medium
(v1) |
9 | 1145-1148 | 3)
From the above equation, we get the important result
that if r < i (i e , if the ray bends toward the normal), the
speed of the light wave in the second medium (v2) will be
less then the speed of the light wave in the first medium
(v1) This prediction is opposite to the prediction from
the corpuscular model of light and as later experiments
showed, the prediction of the wave theory is correct |
9 | 1146-1149 | e , if the ray bends toward the normal), the
speed of the light wave in the second medium (v2) will be
less then the speed of the light wave in the first medium
(v1) This prediction is opposite to the prediction from
the corpuscular model of light and as later experiments
showed, the prediction of the wave theory is correct Now,
if c represents the speed of light in vacuum, then,
1
1
c
n
=v
(10 |
9 | 1147-1150 | , if the ray bends toward the normal), the
speed of the light wave in the second medium (v2) will be
less then the speed of the light wave in the first medium
(v1) This prediction is opposite to the prediction from
the corpuscular model of light and as later experiments
showed, the prediction of the wave theory is correct Now,
if c represents the speed of light in vacuum, then,
1
1
c
n
=v
(10 4)
and
n2 =
2
vc
(10 |
9 | 1148-1151 | This prediction is opposite to the prediction from
the corpuscular model of light and as later experiments
showed, the prediction of the wave theory is correct Now,
if c represents the speed of light in vacuum, then,
1
1
c
n
=v
(10 4)
and
n2 =
2
vc
(10 5)
are known as the refractive indices of medium 1 and
medium 2, respectively |
9 | 1149-1152 | Now,
if c represents the speed of light in vacuum, then,
1
1
c
n
=v
(10 4)
and
n2 =
2
vc
(10 5)
are known as the refractive indices of medium 1 and
medium 2, respectively In terms of the refractive indices, Eq |
9 | 1150-1153 | 4)
and
n2 =
2
vc
(10 5)
are known as the refractive indices of medium 1 and
medium 2, respectively In terms of the refractive indices, Eq (10 |
9 | 1151-1154 | 5)
are known as the refractive indices of medium 1 and
medium 2, respectively In terms of the refractive indices, Eq (10 3) can
be written as
n1 sin i = n2 sin r
(10 |
9 | 1152-1155 | In terms of the refractive indices, Eq (10 3) can
be written as
n1 sin i = n2 sin r
(10 6)
This is the Snell’s law of refraction |
9 | 1153-1156 | (10 3) can
be written as
n1 sin i = n2 sin r
(10 6)
This is the Snell’s law of refraction Further, if l1 and l 2 denote the
wavelengths of light in medium 1 and medium 2, respectively and if the
distance BC is equal to l 1 then the distance AE will be equal to l 2 (because
if the crest from B has reached C in time t, then the crest from A should
have also reached E in time t ); thus,
1
1
2
2
BC
AE
v
v
λλ
=
=
or
1
2
1
2
v
v
λ
=λ
(10 |
9 | 1154-1157 | 3) can
be written as
n1 sin i = n2 sin r
(10 6)
This is the Snell’s law of refraction Further, if l1 and l 2 denote the
wavelengths of light in medium 1 and medium 2, respectively and if the
distance BC is equal to l 1 then the distance AE will be equal to l 2 (because
if the crest from B has reached C in time t, then the crest from A should
have also reached E in time t ); thus,
1
1
2
2
BC
AE
v
v
λλ
=
=
or
1
2
1
2
v
v
λ
=λ
(10 7)
CHRISTIAAN HUYGENS (1629 – 1695)
Christiaan Huygens
(1629 – 1695) Dutch
physicist, astronomer,
mathematician and the
founder of the wave
theory of light |
9 | 1155-1158 | 6)
This is the Snell’s law of refraction Further, if l1 and l 2 denote the
wavelengths of light in medium 1 and medium 2, respectively and if the
distance BC is equal to l 1 then the distance AE will be equal to l 2 (because
if the crest from B has reached C in time t, then the crest from A should
have also reached E in time t ); thus,
1
1
2
2
BC
AE
v
v
λλ
=
=
or
1
2
1
2
v
v
λ
=λ
(10 7)
CHRISTIAAN HUYGENS (1629 – 1695)
Christiaan Huygens
(1629 – 1695) Dutch
physicist, astronomer,
mathematician and the
founder of the wave
theory of light His book,
Treatise on light, makes
fascinating reading even
today |
9 | 1156-1159 | Further, if l1 and l 2 denote the
wavelengths of light in medium 1 and medium 2, respectively and if the
distance BC is equal to l 1 then the distance AE will be equal to l 2 (because
if the crest from B has reached C in time t, then the crest from A should
have also reached E in time t ); thus,
1
1
2
2
BC
AE
v
v
λλ
=
=
or
1
2
1
2
v
v
λ
=λ
(10 7)
CHRISTIAAN HUYGENS (1629 – 1695)
Christiaan Huygens
(1629 – 1695) Dutch
physicist, astronomer,
mathematician and the
founder of the wave
theory of light His book,
Treatise on light, makes
fascinating reading even
today He brilliantly
explained the double
refraction shown by the
mineral calcite in this
work in addition to
reflection and refraction |
9 | 1157-1160 | 7)
CHRISTIAAN HUYGENS (1629 – 1695)
Christiaan Huygens
(1629 – 1695) Dutch
physicist, astronomer,
mathematician and the
founder of the wave
theory of light His book,
Treatise on light, makes
fascinating reading even
today He brilliantly
explained the double
refraction shown by the
mineral calcite in this
work in addition to
reflection and refraction He was the first to
analyse circular and
simple harmonic motion
and designed and built
improved clocks and
telescopes |
9 | 1158-1161 | His book,
Treatise on light, makes
fascinating reading even
today He brilliantly
explained the double
refraction shown by the
mineral calcite in this
work in addition to
reflection and refraction He was the first to
analyse circular and
simple harmonic motion
and designed and built
improved clocks and
telescopes He discovered
the true geometry of
Saturn’s rings |
9 | 1159-1162 | He brilliantly
explained the double
refraction shown by the
mineral calcite in this
work in addition to
reflection and refraction He was the first to
analyse circular and
simple harmonic motion
and designed and built
improved clocks and
telescopes He discovered
the true geometry of
Saturn’s rings Rationalised 2023-24
Physics
260
The above equation implies that when a wave gets refracted into a
denser medium (v1 > v2) the wavelength and the speed of propagation
decrease but the frequency n (= v/l) remains the same |
9 | 1160-1163 | He was the first to
analyse circular and
simple harmonic motion
and designed and built
improved clocks and
telescopes He discovered
the true geometry of
Saturn’s rings Rationalised 2023-24
Physics
260
The above equation implies that when a wave gets refracted into a
denser medium (v1 > v2) the wavelength and the speed of propagation
decrease but the frequency n (= v/l) remains the same 10 |
9 | 1161-1164 | He discovered
the true geometry of
Saturn’s rings Rationalised 2023-24
Physics
260
The above equation implies that when a wave gets refracted into a
denser medium (v1 > v2) the wavelength and the speed of propagation
decrease but the frequency n (= v/l) remains the same 10 3 |
9 | 1162-1165 | Rationalised 2023-24
Physics
260
The above equation implies that when a wave gets refracted into a
denser medium (v1 > v2) the wavelength and the speed of propagation
decrease but the frequency n (= v/l) remains the same 10 3 2 Refraction at a rarer medium
We now consider refraction of a plane wave at a rarer medium, i |
9 | 1163-1166 | 10 3 2 Refraction at a rarer medium
We now consider refraction of a plane wave at a rarer medium, i e |
9 | 1164-1167 | 3 2 Refraction at a rarer medium
We now consider refraction of a plane wave at a rarer medium, i e ,
v2 > v1 |
9 | 1165-1168 | 2 Refraction at a rarer medium
We now consider refraction of a plane wave at a rarer medium, i e ,
v2 > v1 Proceeding in an exactly similar manner we can construct a
refracted wavefront as shown in Fig |
9 | 1166-1169 | e ,
v2 > v1 Proceeding in an exactly similar manner we can construct a
refracted wavefront as shown in Fig 10 |
9 | 1167-1170 | ,
v2 > v1 Proceeding in an exactly similar manner we can construct a
refracted wavefront as shown in Fig 10 5 |
9 | 1168-1171 | Proceeding in an exactly similar manner we can construct a
refracted wavefront as shown in Fig 10 5 The angle of refraction
will now be greater than angle of incidence; however, we will still have
n1 sin i = n2 sin r |
9 | 1169-1172 | 10 5 The angle of refraction
will now be greater than angle of incidence; however, we will still have
n1 sin i = n2 sin r We define an angle ic by the following equation
2
1
sin c
n
i
=n
(10 |
9 | 1170-1173 | 5 The angle of refraction
will now be greater than angle of incidence; however, we will still have
n1 sin i = n2 sin r We define an angle ic by the following equation
2
1
sin c
n
i
=n
(10 8)
Thus, if i = ic then sin r = 1 and r = 90° |
9 | 1171-1174 | The angle of refraction
will now be greater than angle of incidence; however, we will still have
n1 sin i = n2 sin r We define an angle ic by the following equation
2
1
sin c
n
i
=n
(10 8)
Thus, if i = ic then sin r = 1 and r = 90° Obviously, for i > ic, there can
not be any refracted wave |
9 | 1172-1175 | We define an angle ic by the following equation
2
1
sin c
n
i
=n
(10 8)
Thus, if i = ic then sin r = 1 and r = 90° Obviously, for i > ic, there can
not be any refracted wave The angle ic is known as the critical angle and
for all angles of incidence greater than the critical angle, we will not have
any refracted wave and the wave will undergo what is known as total
internal reflection |
9 | 1173-1176 | 8)
Thus, if i = ic then sin r = 1 and r = 90° Obviously, for i > ic, there can
not be any refracted wave The angle ic is known as the critical angle and
for all angles of incidence greater than the critical angle, we will not have
any refracted wave and the wave will undergo what is known as total
internal reflection The phenomenon of total internal reflection and its
applications was discussed in Section 9 |
9 | 1174-1177 | Obviously, for i > ic, there can
not be any refracted wave The angle ic is known as the critical angle and
for all angles of incidence greater than the critical angle, we will not have
any refracted wave and the wave will undergo what is known as total
internal reflection The phenomenon of total internal reflection and its
applications was discussed in Section 9 4 |
9 | 1175-1178 | The angle ic is known as the critical angle and
for all angles of incidence greater than the critical angle, we will not have
any refracted wave and the wave will undergo what is known as total
internal reflection The phenomenon of total internal reflection and its
applications was discussed in Section 9 4 Demonstration of interference, diffraction, refraction, resonance and Doppler effect
http://www |
9 | 1176-1179 | The phenomenon of total internal reflection and its
applications was discussed in Section 9 4 Demonstration of interference, diffraction, refraction, resonance and Doppler effect
http://www falstad |
9 | 1177-1180 | 4 Demonstration of interference, diffraction, refraction, resonance and Doppler effect
http://www falstad com/ripple/
FIGURE 10 |
9 | 1178-1181 | Demonstration of interference, diffraction, refraction, resonance and Doppler effect
http://www falstad com/ripple/
FIGURE 10 5 Refraction of a plane wave incident on a
rarer medium for which v2 > v1 |
9 | 1179-1182 | falstad com/ripple/
FIGURE 10 5 Refraction of a plane wave incident on a
rarer medium for which v2 > v1 The plane wave bends
away from the normal |
9 | 1180-1183 | com/ripple/
FIGURE 10 5 Refraction of a plane wave incident on a
rarer medium for which v2 > v1 The plane wave bends
away from the normal 10 |
9 | 1181-1184 | 5 Refraction of a plane wave incident on a
rarer medium for which v2 > v1 The plane wave bends
away from the normal 10 3 |
9 | 1182-1185 | The plane wave bends
away from the normal 10 3 3 Reflection of a plane wave by a plane surface
We next consider a plane wave AB incident at an angle i on a reflecting
surface MN |
9 | 1183-1186 | 10 3 3 Reflection of a plane wave by a plane surface
We next consider a plane wave AB incident at an angle i on a reflecting
surface MN If v represents the speed of the wave in the medium and if t
represents the time taken by the wavefront to advance from the point B
to C then the distance
BC = vt
In order to construct the reflected wavefront we draw a sphere of
radius vt from the point A as shown in Fig |
9 | 1184-1187 | 3 3 Reflection of a plane wave by a plane surface
We next consider a plane wave AB incident at an angle i on a reflecting
surface MN If v represents the speed of the wave in the medium and if t
represents the time taken by the wavefront to advance from the point B
to C then the distance
BC = vt
In order to construct the reflected wavefront we draw a sphere of
radius vt from the point A as shown in Fig 10 |
9 | 1185-1188 | 3 Reflection of a plane wave by a plane surface
We next consider a plane wave AB incident at an angle i on a reflecting
surface MN If v represents the speed of the wave in the medium and if t
represents the time taken by the wavefront to advance from the point B
to C then the distance
BC = vt
In order to construct the reflected wavefront we draw a sphere of
radius vt from the point A as shown in Fig 10 6 |
9 | 1186-1189 | If v represents the speed of the wave in the medium and if t
represents the time taken by the wavefront to advance from the point B
to C then the distance
BC = vt
In order to construct the reflected wavefront we draw a sphere of
radius vt from the point A as shown in Fig 10 6 Let CE represent the
tangent plane drawn from the point C to this sphere |
9 | 1187-1190 | 10 6 Let CE represent the
tangent plane drawn from the point C to this sphere Obviously
AE = BC = vt
Rationalised 2023-24
261
Wave Optics
FIGURE 10 |
9 | 1188-1191 | 6 Let CE represent the
tangent plane drawn from the point C to this sphere Obviously
AE = BC = vt
Rationalised 2023-24
261
Wave Optics
FIGURE 10 6 Reflection of a plane wave AB by the reflecting surface MN |
9 | 1189-1192 | Let CE represent the
tangent plane drawn from the point C to this sphere Obviously
AE = BC = vt
Rationalised 2023-24
261
Wave Optics
FIGURE 10 6 Reflection of a plane wave AB by the reflecting surface MN AB and CE represent incident and reflected wavefronts |
9 | 1190-1193 | Obviously
AE = BC = vt
Rationalised 2023-24
261
Wave Optics
FIGURE 10 6 Reflection of a plane wave AB by the reflecting surface MN AB and CE represent incident and reflected wavefronts FIGURE 10 |
9 | 1191-1194 | 6 Reflection of a plane wave AB by the reflecting surface MN AB and CE represent incident and reflected wavefronts FIGURE 10 7 Refraction of a plane wave by (a) a thin prism, (b) a convex lens |
9 | 1192-1195 | AB and CE represent incident and reflected wavefronts FIGURE 10 7 Refraction of a plane wave by (a) a thin prism, (b) a convex lens (c) Reflection of a plane wave by a concave mirror |
9 | 1193-1196 | FIGURE 10 7 Refraction of a plane wave by (a) a thin prism, (b) a convex lens (c) Reflection of a plane wave by a concave mirror If we now consider the triangles EAC and BAC we will find that they
are congruent and therefore, the angles i and r (as shown in Fig |
9 | 1194-1197 | 7 Refraction of a plane wave by (a) a thin prism, (b) a convex lens (c) Reflection of a plane wave by a concave mirror If we now consider the triangles EAC and BAC we will find that they
are congruent and therefore, the angles i and r (as shown in Fig 10 |
9 | 1195-1198 | (c) Reflection of a plane wave by a concave mirror If we now consider the triangles EAC and BAC we will find that they
are congruent and therefore, the angles i and r (as shown in Fig 10 6)
would be equal |
9 | 1196-1199 | If we now consider the triangles EAC and BAC we will find that they
are congruent and therefore, the angles i and r (as shown in Fig 10 6)
would be equal This is the law of reflection |
9 | 1197-1200 | 10 6)
would be equal This is the law of reflection Once we have the laws of reflection and refraction, the behaviour of
prisms, lenses, and mirrors can be understood |
9 | 1198-1201 | 6)
would be equal This is the law of reflection Once we have the laws of reflection and refraction, the behaviour of
prisms, lenses, and mirrors can be understood These phenomena were
discussed in detail in Chapter 9 on the basis of rectilinear propagation of
light |
9 | 1199-1202 | This is the law of reflection Once we have the laws of reflection and refraction, the behaviour of
prisms, lenses, and mirrors can be understood These phenomena were
discussed in detail in Chapter 9 on the basis of rectilinear propagation of
light Here we just describe the behaviour of the wavefronts as they
undergo reflection or refraction |
9 | 1200-1203 | Once we have the laws of reflection and refraction, the behaviour of
prisms, lenses, and mirrors can be understood These phenomena were
discussed in detail in Chapter 9 on the basis of rectilinear propagation of
light Here we just describe the behaviour of the wavefronts as they
undergo reflection or refraction In Fig |
9 | 1201-1204 | These phenomena were
discussed in detail in Chapter 9 on the basis of rectilinear propagation of
light Here we just describe the behaviour of the wavefronts as they
undergo reflection or refraction In Fig 10 |
9 | 1202-1205 | Here we just describe the behaviour of the wavefronts as they
undergo reflection or refraction In Fig 10 7(a) we consider a plane wave
passing through a thin prism |
9 | 1203-1206 | In Fig 10 7(a) we consider a plane wave
passing through a thin prism Clearly, since the speed of light waves is
less in glass, the lower portion of the incoming wavefront (which travels
through the greatest thickness of glass) will get delayed resulting in a tilt
in the emerging wavefront as shown in the figure |
9 | 1204-1207 | 10 7(a) we consider a plane wave
passing through a thin prism Clearly, since the speed of light waves is
less in glass, the lower portion of the incoming wavefront (which travels
through the greatest thickness of glass) will get delayed resulting in a tilt
in the emerging wavefront as shown in the figure In Fig |
9 | 1205-1208 | 7(a) we consider a plane wave
passing through a thin prism Clearly, since the speed of light waves is
less in glass, the lower portion of the incoming wavefront (which travels
through the greatest thickness of glass) will get delayed resulting in a tilt
in the emerging wavefront as shown in the figure In Fig 10 |
9 | 1206-1209 | Clearly, since the speed of light waves is
less in glass, the lower portion of the incoming wavefront (which travels
through the greatest thickness of glass) will get delayed resulting in a tilt
in the emerging wavefront as shown in the figure In Fig 10 7(b) we
consider a plane wave incident on a thin convex lens; the central part of
the incident plane wave traverses the thickest portion of the lens and is
delayed the most |
9 | 1207-1210 | In Fig 10 7(b) we
consider a plane wave incident on a thin convex lens; the central part of
the incident plane wave traverses the thickest portion of the lens and is
delayed the most The emerging wavefront has a depression at the centre
and therefore the wavefront becomes spherical and converges to the point
F which is known as the focus |
9 | 1208-1211 | 10 7(b) we
consider a plane wave incident on a thin convex lens; the central part of
the incident plane wave traverses the thickest portion of the lens and is
delayed the most The emerging wavefront has a depression at the centre
and therefore the wavefront becomes spherical and converges to the point
F which is known as the focus In Fig |
9 | 1209-1212 | 7(b) we
consider a plane wave incident on a thin convex lens; the central part of
the incident plane wave traverses the thickest portion of the lens and is
delayed the most The emerging wavefront has a depression at the centre
and therefore the wavefront becomes spherical and converges to the point
F which is known as the focus In Fig 10 |
9 | 1210-1213 | The emerging wavefront has a depression at the centre
and therefore the wavefront becomes spherical and converges to the point
F which is known as the focus In Fig 10 7(c) a plane wave is incident on
a concave mirror and on reflection we have a spherical wave converging
to the focal point F |
9 | 1211-1214 | In Fig 10 7(c) a plane wave is incident on
a concave mirror and on reflection we have a spherical wave converging
to the focal point F In a similar manner, we can understand refraction
and reflection by concave lenses and convex mirrors |
9 | 1212-1215 | 10 7(c) a plane wave is incident on
a concave mirror and on reflection we have a spherical wave converging
to the focal point F In a similar manner, we can understand refraction
and reflection by concave lenses and convex mirrors From the above discussion it follows that the total time taken from a
point on the object to the corresponding point on the image is the same
measured along any ray |
9 | 1213-1216 | 7(c) a plane wave is incident on
a concave mirror and on reflection we have a spherical wave converging
to the focal point F In a similar manner, we can understand refraction
and reflection by concave lenses and convex mirrors From the above discussion it follows that the total time taken from a
point on the object to the corresponding point on the image is the same
measured along any ray For example, when a convex lens focusses light
to form a real image, although the ray going through the centre traverses
a shorter path, but because of the slower speed in glass, the time taken
is the same as for rays travelling near the edge of the lens |
9 | 1214-1217 | In a similar manner, we can understand refraction
and reflection by concave lenses and convex mirrors From the above discussion it follows that the total time taken from a
point on the object to the corresponding point on the image is the same
measured along any ray For example, when a convex lens focusses light
to form a real image, although the ray going through the centre traverses
a shorter path, but because of the slower speed in glass, the time taken
is the same as for rays travelling near the edge of the lens Rationalised 2023-24
Physics
262
10 |
9 | 1215-1218 | From the above discussion it follows that the total time taken from a
point on the object to the corresponding point on the image is the same
measured along any ray For example, when a convex lens focusses light
to form a real image, although the ray going through the centre traverses
a shorter path, but because of the slower speed in glass, the time taken
is the same as for rays travelling near the edge of the lens Rationalised 2023-24
Physics
262
10 4 COHERENT AND INCOHERENT
ADDITION OF WAVES
In this section we will discuss the
interference pattern produced by the
superposition of two waves |
9 | 1216-1219 | For example, when a convex lens focusses light
to form a real image, although the ray going through the centre traverses
a shorter path, but because of the slower speed in glass, the time taken
is the same as for rays travelling near the edge of the lens Rationalised 2023-24
Physics
262
10 4 COHERENT AND INCOHERENT
ADDITION OF WAVES
In this section we will discuss the
interference pattern produced by the
superposition of two waves You may recall
that we had discussed the superposition
principle in Chapter 14 of your Class XI
textbook |
9 | 1217-1220 | Rationalised 2023-24
Physics
262
10 4 COHERENT AND INCOHERENT
ADDITION OF WAVES
In this section we will discuss the
interference pattern produced by the
superposition of two waves You may recall
that we had discussed the superposition
principle in Chapter 14 of your Class XI
textbook Indeed the entire field of
interference is based on the superposition
principle according to which at a particular
point in the medium, the resultant
displacement produced by a number of
waves is the vector sum of the displace-
ments produced by each of the waves |
9 | 1218-1221 | 4 COHERENT AND INCOHERENT
ADDITION OF WAVES
In this section we will discuss the
interference pattern produced by the
superposition of two waves You may recall
that we had discussed the superposition
principle in Chapter 14 of your Class XI
textbook Indeed the entire field of
interference is based on the superposition
principle according to which at a particular
point in the medium, the resultant
displacement produced by a number of
waves is the vector sum of the displace-
ments produced by each of the waves Consider two needles S1 and S2 moving
periodically up and down in an identical
fashion in a trough of water [Fig |
9 | 1219-1222 | You may recall
that we had discussed the superposition
principle in Chapter 14 of your Class XI
textbook Indeed the entire field of
interference is based on the superposition
principle according to which at a particular
point in the medium, the resultant
displacement produced by a number of
waves is the vector sum of the displace-
ments produced by each of the waves Consider two needles S1 and S2 moving
periodically up and down in an identical
fashion in a trough of water [Fig 10 |
9 | 1220-1223 | Indeed the entire field of
interference is based on the superposition
principle according to which at a particular
point in the medium, the resultant
displacement produced by a number of
waves is the vector sum of the displace-
ments produced by each of the waves Consider two needles S1 and S2 moving
periodically up and down in an identical
fashion in a trough of water [Fig 10 8(a)] |
9 | 1221-1224 | Consider two needles S1 and S2 moving
periodically up and down in an identical
fashion in a trough of water [Fig 10 8(a)] They produce two water waves,
and at a particular point, the phase difference between the displacements
produced by each of the waves does not change with time; when this
happens the two sources are said to be coherent |
9 | 1222-1225 | 10 8(a)] They produce two water waves,
and at a particular point, the phase difference between the displacements
produced by each of the waves does not change with time; when this
happens the two sources are said to be coherent Figure 10 |
9 | 1223-1226 | 8(a)] They produce two water waves,
and at a particular point, the phase difference between the displacements
produced by each of the waves does not change with time; when this
happens the two sources are said to be coherent Figure 10 8(b) shows
the position of crests (solid circles) and troughs (dashed circles) at a given
instant of time |
9 | 1224-1227 | They produce two water waves,
and at a particular point, the phase difference between the displacements
produced by each of the waves does not change with time; when this
happens the two sources are said to be coherent Figure 10 8(b) shows
the position of crests (solid circles) and troughs (dashed circles) at a given
instant of time Consider a point P for which
S1 P = S2 P
EXAMPLE 10 |
9 | 1225-1228 | Figure 10 8(b) shows
the position of crests (solid circles) and troughs (dashed circles) at a given
instant of time Consider a point P for which
S1 P = S2 P
EXAMPLE 10 1
Example 10 |
9 | 1226-1229 | 8(b) shows
the position of crests (solid circles) and troughs (dashed circles) at a given
instant of time Consider a point P for which
S1 P = S2 P
EXAMPLE 10 1
Example 10 1
(a)
When monochromatic light is incident on a surface separating
two media, the reflected and refracted light both have the same
frequency as the incident frequency |
9 | 1227-1230 | Consider a point P for which
S1 P = S2 P
EXAMPLE 10 1
Example 10 1
(a)
When monochromatic light is incident on a surface separating
two media, the reflected and refracted light both have the same
frequency as the incident frequency Explain why |
9 | 1228-1231 | 1
Example 10 1
(a)
When monochromatic light is incident on a surface separating
two media, the reflected and refracted light both have the same
frequency as the incident frequency Explain why (b)
When light travels from a rarer to a denser medium, the speed
decreases |
9 | 1229-1232 | 1
(a)
When monochromatic light is incident on a surface separating
two media, the reflected and refracted light both have the same
frequency as the incident frequency Explain why (b)
When light travels from a rarer to a denser medium, the speed
decreases Does the reduction in speed imply a reduction in the
energy carried by the light wave |
9 | 1230-1233 | Explain why (b)
When light travels from a rarer to a denser medium, the speed
decreases Does the reduction in speed imply a reduction in the
energy carried by the light wave (c)
In the wave picture of light, intensity of light is determined by the
square of the amplitude of the wave |
9 | 1231-1234 | (b)
When light travels from a rarer to a denser medium, the speed
decreases Does the reduction in speed imply a reduction in the
energy carried by the light wave (c)
In the wave picture of light, intensity of light is determined by the
square of the amplitude of the wave What determines the intensity
of light in the photon picture of light |
9 | 1232-1235 | Does the reduction in speed imply a reduction in the
energy carried by the light wave (c)
In the wave picture of light, intensity of light is determined by the
square of the amplitude of the wave What determines the intensity
of light in the photon picture of light Solution
(a)
Reflection and refraction arise through interaction of incident light
with the atomic constituents of matter |
9 | 1233-1236 | (c)
In the wave picture of light, intensity of light is determined by the
square of the amplitude of the wave What determines the intensity
of light in the photon picture of light Solution
(a)
Reflection and refraction arise through interaction of incident light
with the atomic constituents of matter Atoms may be viewed as
oscillators, which take up the frequency of the external agency
(light) causing forced oscillations |
9 | 1234-1237 | What determines the intensity
of light in the photon picture of light Solution
(a)
Reflection and refraction arise through interaction of incident light
with the atomic constituents of matter Atoms may be viewed as
oscillators, which take up the frequency of the external agency
(light) causing forced oscillations The frequency of light emitted by
a charged oscillator equals its frequency of oscillation |
9 | 1235-1238 | Solution
(a)
Reflection and refraction arise through interaction of incident light
with the atomic constituents of matter Atoms may be viewed as
oscillators, which take up the frequency of the external agency
(light) causing forced oscillations The frequency of light emitted by
a charged oscillator equals its frequency of oscillation Thus, the
frequency of scattered light equals the frequency of incident light |
9 | 1236-1239 | Atoms may be viewed as
oscillators, which take up the frequency of the external agency
(light) causing forced oscillations The frequency of light emitted by
a charged oscillator equals its frequency of oscillation Thus, the
frequency of scattered light equals the frequency of incident light (b)
No |
9 | 1237-1240 | The frequency of light emitted by
a charged oscillator equals its frequency of oscillation Thus, the
frequency of scattered light equals the frequency of incident light (b)
No Energy carried by a wave depends on the amplitude of the
wave, not on the speed of wave propagation |
9 | 1238-1241 | Thus, the
frequency of scattered light equals the frequency of incident light (b)
No Energy carried by a wave depends on the amplitude of the
wave, not on the speed of wave propagation (c)
For a given frequency, intensity of light in the photon picture is
determined by the number of photons crossing an unit area per
unit time |
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