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9 | 39-42 | 9 2 1 Sign convention
To derive the relevant formulae for
reflection by spherical mirrors and
refraction by spherical lenses, we must
first adopt a sign convention for
measuring distances In this book, we
shall follow the Cartesian sign
convention |
9 | 40-43 | 2 1 Sign convention
To derive the relevant formulae for
reflection by spherical mirrors and
refraction by spherical lenses, we must
first adopt a sign convention for
measuring distances In this book, we
shall follow the Cartesian sign
convention According to this
convention, all distances are measured
from the pole of the mirror or the optical
centre of the lens |
9 | 41-44 | 1 Sign convention
To derive the relevant formulae for
reflection by spherical mirrors and
refraction by spherical lenses, we must
first adopt a sign convention for
measuring distances In this book, we
shall follow the Cartesian sign
convention According to this
convention, all distances are measured
from the pole of the mirror or the optical
centre of the lens The distances
measured in the same direction as the
incident light are taken as positive and
those measured in the direction
opposite to the direction of incident light are taken as negative (Fig |
9 | 42-45 | In this book, we
shall follow the Cartesian sign
convention According to this
convention, all distances are measured
from the pole of the mirror or the optical
centre of the lens The distances
measured in the same direction as the
incident light are taken as positive and
those measured in the direction
opposite to the direction of incident light are taken as negative (Fig 9 |
9 | 43-46 | According to this
convention, all distances are measured
from the pole of the mirror or the optical
centre of the lens The distances
measured in the same direction as the
incident light are taken as positive and
those measured in the direction
opposite to the direction of incident light are taken as negative (Fig 9 2) |
9 | 44-47 | The distances
measured in the same direction as the
incident light are taken as positive and
those measured in the direction
opposite to the direction of incident light are taken as negative (Fig 9 2) The heights measured upwards with respect to x-axis and normal to the
Rationalised 2023-24
Ray Optics and
Optical Instruments
223
principal axis (x-axis) of the mirror/lens are taken as positive (Fig |
9 | 45-48 | 9 2) The heights measured upwards with respect to x-axis and normal to the
Rationalised 2023-24
Ray Optics and
Optical Instruments
223
principal axis (x-axis) of the mirror/lens are taken as positive (Fig 9 |
9 | 46-49 | 2) The heights measured upwards with respect to x-axis and normal to the
Rationalised 2023-24
Ray Optics and
Optical Instruments
223
principal axis (x-axis) of the mirror/lens are taken as positive (Fig 9 2) |
9 | 47-50 | The heights measured upwards with respect to x-axis and normal to the
Rationalised 2023-24
Ray Optics and
Optical Instruments
223
principal axis (x-axis) of the mirror/lens are taken as positive (Fig 9 2) The heights measured downwards are taken as negative |
9 | 48-51 | 9 2) The heights measured downwards are taken as negative With a common accepted convention, it turns out that a single formula
for spherical mirrors and a single formula for spherical lenses can handle
all different cases |
9 | 49-52 | 2) The heights measured downwards are taken as negative With a common accepted convention, it turns out that a single formula
for spherical mirrors and a single formula for spherical lenses can handle
all different cases 9 |
9 | 50-53 | The heights measured downwards are taken as negative With a common accepted convention, it turns out that a single formula
for spherical mirrors and a single formula for spherical lenses can handle
all different cases 9 2 |
9 | 51-54 | With a common accepted convention, it turns out that a single formula
for spherical mirrors and a single formula for spherical lenses can handle
all different cases 9 2 2 Focal length of spherical mirrors
Figure 9 |
9 | 52-55 | 9 2 2 Focal length of spherical mirrors
Figure 9 3 shows what happens when a parallel beam of light is incident
on (a) a concave mirror, and (b) a convex mirror |
9 | 53-56 | 2 2 Focal length of spherical mirrors
Figure 9 3 shows what happens when a parallel beam of light is incident
on (a) a concave mirror, and (b) a convex mirror We assume that the rays
are paraxial, i |
9 | 54-57 | 2 Focal length of spherical mirrors
Figure 9 3 shows what happens when a parallel beam of light is incident
on (a) a concave mirror, and (b) a convex mirror We assume that the rays
are paraxial, i e |
9 | 55-58 | 3 shows what happens when a parallel beam of light is incident
on (a) a concave mirror, and (b) a convex mirror We assume that the rays
are paraxial, i e , they are incident at points close to the pole P of the mirror
and make small angles with the principal axis |
9 | 56-59 | We assume that the rays
are paraxial, i e , they are incident at points close to the pole P of the mirror
and make small angles with the principal axis The reflected rays converge
at a point F on the principal axis of a concave mirror [Fig |
9 | 57-60 | e , they are incident at points close to the pole P of the mirror
and make small angles with the principal axis The reflected rays converge
at a point F on the principal axis of a concave mirror [Fig 9 |
9 | 58-61 | , they are incident at points close to the pole P of the mirror
and make small angles with the principal axis The reflected rays converge
at a point F on the principal axis of a concave mirror [Fig 9 3(a)] |
9 | 59-62 | The reflected rays converge
at a point F on the principal axis of a concave mirror [Fig 9 3(a)] For a convex mirror, the reflected rays appear to diverge from a point F
on its principal axis [Fig |
9 | 60-63 | 9 3(a)] For a convex mirror, the reflected rays appear to diverge from a point F
on its principal axis [Fig 9 |
9 | 61-64 | 3(a)] For a convex mirror, the reflected rays appear to diverge from a point F
on its principal axis [Fig 9 3(b)] |
9 | 62-65 | For a convex mirror, the reflected rays appear to diverge from a point F
on its principal axis [Fig 9 3(b)] The point F is called the principal focus
of the mirror |
9 | 63-66 | 9 3(b)] The point F is called the principal focus
of the mirror If the parallel paraxial beam of light were incident, making
some angle with the principal axis, the reflected rays would converge (or
appear to diverge) from a point in a plane through F normal to the principal
axis |
9 | 64-67 | 3(b)] The point F is called the principal focus
of the mirror If the parallel paraxial beam of light were incident, making
some angle with the principal axis, the reflected rays would converge (or
appear to diverge) from a point in a plane through F normal to the principal
axis This is called the focal plane of the mirror [Fig |
9 | 65-68 | The point F is called the principal focus
of the mirror If the parallel paraxial beam of light were incident, making
some angle with the principal axis, the reflected rays would converge (or
appear to diverge) from a point in a plane through F normal to the principal
axis This is called the focal plane of the mirror [Fig 9 |
9 | 66-69 | If the parallel paraxial beam of light were incident, making
some angle with the principal axis, the reflected rays would converge (or
appear to diverge) from a point in a plane through F normal to the principal
axis This is called the focal plane of the mirror [Fig 9 3(c)] |
9 | 67-70 | This is called the focal plane of the mirror [Fig 9 3(c)] FIGURE 9 |
9 | 68-71 | 9 3(c)] FIGURE 9 3 Focus of a concave and convex mirror |
9 | 69-72 | 3(c)] FIGURE 9 3 Focus of a concave and convex mirror The distance between the focus F and the pole P of the mirror is called
the focal length of the mirror, denoted by f |
9 | 70-73 | FIGURE 9 3 Focus of a concave and convex mirror The distance between the focus F and the pole P of the mirror is called
the focal length of the mirror, denoted by f We now show that f = R/2,
where R is the radius of curvature of the mirror |
9 | 71-74 | 3 Focus of a concave and convex mirror The distance between the focus F and the pole P of the mirror is called
the focal length of the mirror, denoted by f We now show that f = R/2,
where R is the radius of curvature of the mirror The geometry of reflection
of an incident ray is shown in Fig |
9 | 72-75 | The distance between the focus F and the pole P of the mirror is called
the focal length of the mirror, denoted by f We now show that f = R/2,
where R is the radius of curvature of the mirror The geometry of reflection
of an incident ray is shown in Fig 9 |
9 | 73-76 | We now show that f = R/2,
where R is the radius of curvature of the mirror The geometry of reflection
of an incident ray is shown in Fig 9 4 |
9 | 74-77 | The geometry of reflection
of an incident ray is shown in Fig 9 4 Let C be the centre of curvature of the mirror |
9 | 75-78 | 9 4 Let C be the centre of curvature of the mirror Consider a ray parallel
to the principal axis striking the mirror at M |
9 | 76-79 | 4 Let C be the centre of curvature of the mirror Consider a ray parallel
to the principal axis striking the mirror at M Then CM will be
perpendicular to the mirror at M |
9 | 77-80 | Let C be the centre of curvature of the mirror Consider a ray parallel
to the principal axis striking the mirror at M Then CM will be
perpendicular to the mirror at M Let q be the angle of incidence, and MD
Rationalised 2023-24
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224
be the perpendicular from M on the principal axis |
9 | 78-81 | Consider a ray parallel
to the principal axis striking the mirror at M Then CM will be
perpendicular to the mirror at M Let q be the angle of incidence, and MD
Rationalised 2023-24
Physics
224
be the perpendicular from M on the principal axis Then,
ÐMCP = q and ÐMFP = 2q
Now,
tanq =
MD
CD and tan 2q =
MD
FD
(9 |
9 | 79-82 | Then CM will be
perpendicular to the mirror at M Let q be the angle of incidence, and MD
Rationalised 2023-24
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224
be the perpendicular from M on the principal axis Then,
ÐMCP = q and ÐMFP = 2q
Now,
tanq =
MD
CD and tan 2q =
MD
FD
(9 1)
For small q, which is true for paraxial rays, tanq » q,
tan 2q » 2q |
9 | 80-83 | Let q be the angle of incidence, and MD
Rationalised 2023-24
Physics
224
be the perpendicular from M on the principal axis Then,
ÐMCP = q and ÐMFP = 2q
Now,
tanq =
MD
CD and tan 2q =
MD
FD
(9 1)
For small q, which is true for paraxial rays, tanq » q,
tan 2q » 2q Therefore, Eq |
9 | 81-84 | Then,
ÐMCP = q and ÐMFP = 2q
Now,
tanq =
MD
CD and tan 2q =
MD
FD
(9 1)
For small q, which is true for paraxial rays, tanq » q,
tan 2q » 2q Therefore, Eq (9 |
9 | 82-85 | 1)
For small q, which is true for paraxial rays, tanq » q,
tan 2q » 2q Therefore, Eq (9 1) gives
MD
FD = 2
MD
CD
or, FD =
CD
2
(9 |
9 | 83-86 | Therefore, Eq (9 1) gives
MD
FD = 2
MD
CD
or, FD =
CD
2
(9 2)
Now, for small q, the point D is very close to the point P |
9 | 84-87 | (9 1) gives
MD
FD = 2
MD
CD
or, FD =
CD
2
(9 2)
Now, for small q, the point D is very close to the point P Therefore, FD = f and CD = R |
9 | 85-88 | 1) gives
MD
FD = 2
MD
CD
or, FD =
CD
2
(9 2)
Now, for small q, the point D is very close to the point P Therefore, FD = f and CD = R Equation (9 |
9 | 86-89 | 2)
Now, for small q, the point D is very close to the point P Therefore, FD = f and CD = R Equation (9 2) then gives
f = R/2
(9 |
9 | 87-90 | Therefore, FD = f and CD = R Equation (9 2) then gives
f = R/2
(9 3)
9 |
9 | 88-91 | Equation (9 2) then gives
f = R/2
(9 3)
9 2 |
9 | 89-92 | 2) then gives
f = R/2
(9 3)
9 2 3 The mirror equation
If rays emanating from a point actually meet at another point
after reflection and/or refraction, that point is called the image
of the first point |
9 | 90-93 | 3)
9 2 3 The mirror equation
If rays emanating from a point actually meet at another point
after reflection and/or refraction, that point is called the image
of the first point The image is real if the rays actually converge
to the point; it is virtual if the rays do not actually meet but
appear to diverge from the point when produced
backwards |
9 | 91-94 | 2 3 The mirror equation
If rays emanating from a point actually meet at another point
after reflection and/or refraction, that point is called the image
of the first point The image is real if the rays actually converge
to the point; it is virtual if the rays do not actually meet but
appear to diverge from the point when produced
backwards An image is thus a point-to-point
correspondence with the object established through
reflection and/or refraction |
9 | 92-95 | 3 The mirror equation
If rays emanating from a point actually meet at another point
after reflection and/or refraction, that point is called the image
of the first point The image is real if the rays actually converge
to the point; it is virtual if the rays do not actually meet but
appear to diverge from the point when produced
backwards An image is thus a point-to-point
correspondence with the object established through
reflection and/or refraction In principle, we can take any two rays emanating
from a point on an object, trace their paths, find their
point of intersection and thus, obtain the image of
the point due to reflection at a spherical mirror |
9 | 93-96 | The image is real if the rays actually converge
to the point; it is virtual if the rays do not actually meet but
appear to diverge from the point when produced
backwards An image is thus a point-to-point
correspondence with the object established through
reflection and/or refraction In principle, we can take any two rays emanating
from a point on an object, trace their paths, find their
point of intersection and thus, obtain the image of
the point due to reflection at a spherical mirror In
practice, however, it is convenient to choose any two
of the following rays:
(i)
The ray from the point which is parallel to the
principal axis |
9 | 94-97 | An image is thus a point-to-point
correspondence with the object established through
reflection and/or refraction In principle, we can take any two rays emanating
from a point on an object, trace their paths, find their
point of intersection and thus, obtain the image of
the point due to reflection at a spherical mirror In
practice, however, it is convenient to choose any two
of the following rays:
(i)
The ray from the point which is parallel to the
principal axis The reflected ray goes through
the focus of the mirror |
9 | 95-98 | In principle, we can take any two rays emanating
from a point on an object, trace their paths, find their
point of intersection and thus, obtain the image of
the point due to reflection at a spherical mirror In
practice, however, it is convenient to choose any two
of the following rays:
(i)
The ray from the point which is parallel to the
principal axis The reflected ray goes through
the focus of the mirror (ii)
The ray passing through the centre of
curvature of a concave mirror or appearing to
pass through it for a convex mirror |
9 | 96-99 | In
practice, however, it is convenient to choose any two
of the following rays:
(i)
The ray from the point which is parallel to the
principal axis The reflected ray goes through
the focus of the mirror (ii)
The ray passing through the centre of
curvature of a concave mirror or appearing to
pass through it for a convex mirror The
reflected ray simply retraces the path |
9 | 97-100 | The reflected ray goes through
the focus of the mirror (ii)
The ray passing through the centre of
curvature of a concave mirror or appearing to
pass through it for a convex mirror The
reflected ray simply retraces the path (iii) The ray passing through (or directed towards) the focus of the concave
mirror or appearing to pass through (or directed towards) the focus
of a convex mirror |
9 | 98-101 | (ii)
The ray passing through the centre of
curvature of a concave mirror or appearing to
pass through it for a convex mirror The
reflected ray simply retraces the path (iii) The ray passing through (or directed towards) the focus of the concave
mirror or appearing to pass through (or directed towards) the focus
of a convex mirror The reflected ray is parallel to the principal axis |
9 | 99-102 | The
reflected ray simply retraces the path (iii) The ray passing through (or directed towards) the focus of the concave
mirror or appearing to pass through (or directed towards) the focus
of a convex mirror The reflected ray is parallel to the principal axis (iv) The ray incident at any angle at the pole |
9 | 100-103 | (iii) The ray passing through (or directed towards) the focus of the concave
mirror or appearing to pass through (or directed towards) the focus
of a convex mirror The reflected ray is parallel to the principal axis (iv) The ray incident at any angle at the pole The reflected ray follows
laws of reflection |
9 | 101-104 | The reflected ray is parallel to the principal axis (iv) The ray incident at any angle at the pole The reflected ray follows
laws of reflection Figure 9 |
9 | 102-105 | (iv) The ray incident at any angle at the pole The reflected ray follows
laws of reflection Figure 9 5 shows the ray diagram considering three rays |
9 | 103-106 | The reflected ray follows
laws of reflection Figure 9 5 shows the ray diagram considering three rays It shows
the image A¢B¢ (in this case, real) of an object AB formed by a concave
mirror |
9 | 104-107 | Figure 9 5 shows the ray diagram considering three rays It shows
the image A¢B¢ (in this case, real) of an object AB formed by a concave
mirror It does not mean that only three rays emanate from the point A |
9 | 105-108 | 5 shows the ray diagram considering three rays It shows
the image A¢B¢ (in this case, real) of an object AB formed by a concave
mirror It does not mean that only three rays emanate from the point A An infinite number of rays emanate from any source, in all directions |
9 | 106-109 | It shows
the image A¢B¢ (in this case, real) of an object AB formed by a concave
mirror It does not mean that only three rays emanate from the point A An infinite number of rays emanate from any source, in all directions Thus, point A¢ is image point of A if every ray originating at point A and
falling on the concave mirror after reflection passes through the point A¢ |
9 | 107-110 | It does not mean that only three rays emanate from the point A An infinite number of rays emanate from any source, in all directions Thus, point A¢ is image point of A if every ray originating at point A and
falling on the concave mirror after reflection passes through the point A¢ FIGURE 9 |
9 | 108-111 | An infinite number of rays emanate from any source, in all directions Thus, point A¢ is image point of A if every ray originating at point A and
falling on the concave mirror after reflection passes through the point A¢ FIGURE 9 4 Geometry of
reflection of an incident ray on
(a) concave spherical mirror,
and (b) convex spherical mirror |
9 | 109-112 | Thus, point A¢ is image point of A if every ray originating at point A and
falling on the concave mirror after reflection passes through the point A¢ FIGURE 9 4 Geometry of
reflection of an incident ray on
(a) concave spherical mirror,
and (b) convex spherical mirror FIGURE 9 |
9 | 110-113 | FIGURE 9 4 Geometry of
reflection of an incident ray on
(a) concave spherical mirror,
and (b) convex spherical mirror FIGURE 9 5 Ray diagram for image
formation by a concave mirror |
9 | 111-114 | 4 Geometry of
reflection of an incident ray on
(a) concave spherical mirror,
and (b) convex spherical mirror FIGURE 9 5 Ray diagram for image
formation by a concave mirror Rationalised 2023-24
Ray Optics and
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225
We now derive the mirror equation or the relation between the object
distance (u), image distance (v) and the focal length ( f ) |
9 | 112-115 | FIGURE 9 5 Ray diagram for image
formation by a concave mirror Rationalised 2023-24
Ray Optics and
Optical Instruments
225
We now derive the mirror equation or the relation between the object
distance (u), image distance (v) and the focal length ( f ) From Fig |
9 | 113-116 | 5 Ray diagram for image
formation by a concave mirror Rationalised 2023-24
Ray Optics and
Optical Instruments
225
We now derive the mirror equation or the relation between the object
distance (u), image distance (v) and the focal length ( f ) From Fig 9 |
9 | 114-117 | Rationalised 2023-24
Ray Optics and
Optical Instruments
225
We now derive the mirror equation or the relation between the object
distance (u), image distance (v) and the focal length ( f ) From Fig 9 5, the two right-angled triangles A¢B¢F and MPF are
similar |
9 | 115-118 | From Fig 9 5, the two right-angled triangles A¢B¢F and MPF are
similar (For paraxial rays, MP can be considered to be a straight line
perpendicular to CP |
9 | 116-119 | 9 5, the two right-angled triangles A¢B¢F and MPF are
similar (For paraxial rays, MP can be considered to be a straight line
perpendicular to CP ) Therefore,
B A
B F
PM
FP
′
′
′
=
or
B A
B F
BA
FP
′
′
′
=
(∵PM = AB)
(9 |
9 | 117-120 | 5, the two right-angled triangles A¢B¢F and MPF are
similar (For paraxial rays, MP can be considered to be a straight line
perpendicular to CP ) Therefore,
B A
B F
PM
FP
′
′
′
=
or
B A
B F
BA
FP
′
′
′
=
(∵PM = AB)
(9 4)
Since Ð APB = Ð A¢PB¢, the right angled triangles A¢B¢P and ABP are
also similar |
9 | 118-121 | (For paraxial rays, MP can be considered to be a straight line
perpendicular to CP ) Therefore,
B A
B F
PM
FP
′
′
′
=
or
B A
B F
BA
FP
′
′
′
=
(∵PM = AB)
(9 4)
Since Ð APB = Ð A¢PB¢, the right angled triangles A¢B¢P and ABP are
also similar Therefore,
B A
B P
B A
B P
′
′
′
=
(9 |
9 | 119-122 | ) Therefore,
B A
B F
PM
FP
′
′
′
=
or
B A
B F
BA
FP
′
′
′
=
(∵PM = AB)
(9 4)
Since Ð APB = Ð A¢PB¢, the right angled triangles A¢B¢P and ABP are
also similar Therefore,
B A
B P
B A
B P
′
′
′
=
(9 5)
Comparing Eqs |
9 | 120-123 | 4)
Since Ð APB = Ð A¢PB¢, the right angled triangles A¢B¢P and ABP are
also similar Therefore,
B A
B P
B A
B P
′
′
′
=
(9 5)
Comparing Eqs (9 |
9 | 121-124 | Therefore,
B A
B P
B A
B P
′
′
′
=
(9 5)
Comparing Eqs (9 4) and (9 |
9 | 122-125 | 5)
Comparing Eqs (9 4) and (9 5), we get
B P – FP
B F
B P
FP
FP
BP
′
′
′
=
=
(9 |
9 | 123-126 | (9 4) and (9 5), we get
B P – FP
B F
B P
FP
FP
BP
′
′
′
=
=
(9 6)
Equation (9 |
9 | 124-127 | 4) and (9 5), we get
B P – FP
B F
B P
FP
FP
BP
′
′
′
=
=
(9 6)
Equation (9 6) is a relation involving magnitude of distances |
9 | 125-128 | 5), we get
B P – FP
B F
B P
FP
FP
BP
′
′
′
=
=
(9 6)
Equation (9 6) is a relation involving magnitude of distances We now
apply the sign convention |
9 | 126-129 | 6)
Equation (9 6) is a relation involving magnitude of distances We now
apply the sign convention We note that light travels from the object to
the mirror MPN |
9 | 127-130 | 6) is a relation involving magnitude of distances We now
apply the sign convention We note that light travels from the object to
the mirror MPN Hence this is taken as the positive direction |
9 | 128-131 | We now
apply the sign convention We note that light travels from the object to
the mirror MPN Hence this is taken as the positive direction To reach
the object AB, image A¢B¢ as well as the focus F from the pole P, we have
to travel opposite to the direction of incident light |
9 | 129-132 | We note that light travels from the object to
the mirror MPN Hence this is taken as the positive direction To reach
the object AB, image A¢B¢ as well as the focus F from the pole P, we have
to travel opposite to the direction of incident light Hence, all the three
will have negative signs |
9 | 130-133 | Hence this is taken as the positive direction To reach
the object AB, image A¢B¢ as well as the focus F from the pole P, we have
to travel opposite to the direction of incident light Hence, all the three
will have negative signs Thus,
B¢ P = –v, FP = –f, BP = –u
Using these in Eq |
9 | 131-134 | To reach
the object AB, image A¢B¢ as well as the focus F from the pole P, we have
to travel opposite to the direction of incident light Hence, all the three
will have negative signs Thus,
B¢ P = –v, FP = –f, BP = –u
Using these in Eq (9 |
9 | 132-135 | Hence, all the three
will have negative signs Thus,
B¢ P = –v, FP = –f, BP = –u
Using these in Eq (9 6), we get
–
–
v–
f
v
f
u
+
= –
or
v–
f
v
f
u
=
v
f
uv
=
+
1
Dividing it by v, we get
1
1
1
v
u
f
+
=
(9 |
9 | 133-136 | Thus,
B¢ P = –v, FP = –f, BP = –u
Using these in Eq (9 6), we get
–
–
v–
f
v
f
u
+
= –
or
v–
f
v
f
u
=
v
f
uv
=
+
1
Dividing it by v, we get
1
1
1
v
u
f
+
=
(9 7)
This relation is known as the mirror equation |
9 | 134-137 | (9 6), we get
–
–
v–
f
v
f
u
+
= –
or
v–
f
v
f
u
=
v
f
uv
=
+
1
Dividing it by v, we get
1
1
1
v
u
f
+
=
(9 7)
This relation is known as the mirror equation The size of the image relative to the size of the object is another
important quantity to consider |
9 | 135-138 | 6), we get
–
–
v–
f
v
f
u
+
= –
or
v–
f
v
f
u
=
v
f
uv
=
+
1
Dividing it by v, we get
1
1
1
v
u
f
+
=
(9 7)
This relation is known as the mirror equation The size of the image relative to the size of the object is another
important quantity to consider We define linear magnification (m) as the
ratio of the height of the image (h¢) to the height of the object (h):
m =
h
h
′
(9 |
9 | 136-139 | 7)
This relation is known as the mirror equation The size of the image relative to the size of the object is another
important quantity to consider We define linear magnification (m) as the
ratio of the height of the image (h¢) to the height of the object (h):
m =
h
h
′
(9 8)
h and h¢ will be taken positive or negative in accordance with the accepted
sign convention |
9 | 137-140 | The size of the image relative to the size of the object is another
important quantity to consider We define linear magnification (m) as the
ratio of the height of the image (h¢) to the height of the object (h):
m =
h
h
′
(9 8)
h and h¢ will be taken positive or negative in accordance with the accepted
sign convention In triangles A¢B¢P and ABP, we have,
B A
B P
BA
BP
′
′
′
=
With the sign convention, this becomes
Rationalised 2023-24
Physics
226
–
–
h
v
h
u
′ = –
so that
m =
–
h
v
h
u
′ =
(9 |
9 | 138-141 | We define linear magnification (m) as the
ratio of the height of the image (h¢) to the height of the object (h):
m =
h
h
′
(9 8)
h and h¢ will be taken positive or negative in accordance with the accepted
sign convention In triangles A¢B¢P and ABP, we have,
B A
B P
BA
BP
′
′
′
=
With the sign convention, this becomes
Rationalised 2023-24
Physics
226
–
–
h
v
h
u
′ = –
so that
m =
–
h
v
h
u
′ =
(9 9)
We have derived here the mirror equation, Eq |
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