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• Terms used for lensesTerms used for lenses• • Images in lensesImages in lenses
12.2 Converging and 12.2 Converging and diverging lensesdiverging lenses
• • Lens formulaLens formula• • Two thin lenses in contactTwo thin lenses in contact• • Linear magnificationLinear magnification
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12.2 Converging and diverging lenses (SB p. 207)
Converging and diverging lenses
Two types of lenses- converging (convex) lens (light rays converge to a point)- diverging (concave) lens (light rays diverge from a point)
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12.2 Converging and diverging lenses (SB p. 207)
Converging and diverging lenses
Converging lens
Diverging lens
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12.2 Converging and diverging lenses (SB p. 207)
Terms used for lenses
Converging lens
Diverging lens
radii of curvature
radii of curvature
centres of curvature
centres of curvature
principal axis
principal axis
optical centre
optical centre
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12.2 Converging and diverging lenses (SB p. 208)
Terms used for lenses
principle focus (F)
principle focus (F)
focal length
focal length
Converging lens
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12.2 Converging and diverging lenses (SB p. 208)
Terms used for lenses
Converging lens focal plane
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12.2 Converging and diverging lenses (SB p. 209)
Terms used for lenses
Diverging lens
Focal length of diverging lens is -ve
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12.2 Converging and diverging lenses (SB p. 209)
Terms used for lenses
Power of a lens- ability to converge parallel rays
f1
min length Focal1lens a ofPower
Unit – dioptre (D) – 1 D = 1 radian per metre
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More to Know 6More to Know 6
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12.2 Converging and diverging lenses (SB p. 209)
Images in lenses
1. Ray diagram- used to determine position and nature of image
Ray 1
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12.2 Converging and diverging lenses (SB p. 210)
Images in lenses
Ray 2
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More to Know 7More to Know 7
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12.2 Converging and diverging lenses (SB p. 210)
Images in lenses
Ray 3
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More to Know 8More to Know 8
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12.2 Converging and diverging lenses (SB p. 211)
Images in lenses
2. Image formed by a converging lens
(a) Object at infinity
at principal focus; inverted, diminished, real image
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12.2 Converging and diverging lenses (SB p. 211)
Images in lenses
2. Image formed by a converging lens
(b) Object distance u greater than 2f
f < v < 2f; inverted, diminished, real image
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12.2 Converging and diverging lenses (SB p. 211)
Images in lenses
2. Image formed by a converging lens
(c) Object distance u = 2f
v = u = 2f; inverted, same size, real image
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12.2 Converging and diverging lenses (SB p. 212)
Images in lenses
2. Image formed by a converging lens
(d) Object distance u between f and 2 f
v > u; inverted, magnified, real image
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12.2 Converging and diverging lenses (SB p. 212)
Images in lenses
2. Image formed by a converging lens
(e) Object at principal focus (u = f)
at infinity; upright, magnified, virtual image
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12.2 Converging and diverging lenses (SB p. 212)
Images in lenses
2. Image formed by a converging lens
(f) Object distance u less than f
upright, magnified, virtual image (as magnifying glass)
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12.2 Converging and diverging lenses (SB p. 213)
Images in lenses
3. Image formed by a diverging lens
upright, diminished, virtual image
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12.2 Converging and diverging lenses (SB p. 213)
Lens formula
Lens formula- used to determine image distance
fvu
ufuvvfvu
fvf
BIPAOPvu
PIPO
BIOA
fvf
BIOA
BIFQPFIFPF
BIPQ
111
)(
)(
lens formula
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12.2 Converging and diverging lenses (SB p. 214)
Lens formula
Note: 1. If the object is real, then the value of u is positive. If the image is real, then the value of v is positive.
2. If the object is virtual, then the value of u is negative. If the image is virtual, then the value of v is negative.
3. The focal length f of a converging lens is positive. The focal length f of a diverging lens is negative.
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12.2 Converging and diverging lenses (SB p. 214)
Lens formula
Real object - Rays diverging from point on object are incident on lens
Virtual object - incident rays converge to point behind lens
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Example 3Example 3
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Example 4Example 4
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12.2 Converging and diverging lenses (SB p. 215)
Two thin lenses in contact
Object (O) producesimage (I’) by lens 1 1
111f'vu
I’ produces image (I) by lens 2 2
111fv'v
21
1111ffvu
21
111fff
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Example 5Example 5
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12.2 Converging and diverging lenses (SB p. 217)
Linear magnification
)(height Object )(height Image
)(ion magnificatLinear o
ihh
m
POPI
AOBI
hh
m o
i
uvm )(ion magnificatLinear
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12.2 Converging and diverging lenses (SB p. 217)
Linear magnification
11
1
:obtain we using and by t throughouformula lens heMultiply t 2.
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111 formula, lens theFrom
:Note
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m
fu
vu
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Example 6Example 6
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Example 7Example 7
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Power of a converging lens
The larger the power of a converging lens, the nearer the emerging rays converged to the lens.
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TextText
12.2 Converging and diverging lenses (SB p. 209)
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Spherical aberration
The light rays near the edges of the lens and near the principal axis do not focus to the same point after refraction This phenomenon is called spherical aberration of lenses.Return to
TextText
12.2 Converging and diverging lenses (SB p. 210)
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Chromatic aberration
Since red light refracts less than violet light in glass (lens), a fringe of colours around the image is formed. The phenomenon is called chromatic aberration. Return to
TextText
12.2 Converging and diverging lenses (SB p. 210)
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Q: Q: An object is at a distance of 20 cm from a converging lens of focal length 12 cm. Where is the image?
Solution
12.2 Converging and diverging lenses (SB p. 214)
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Solution:Solution:
lens. thefrom cm 30 is image The
cm 30201
121111
111
vufv
fvu
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TextText
12.2 Converging and diverging lenses (SB p. 214)
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Q: Q: A converging beam of light incidents on a diverging lens of focal length 18.0 cm. If the beam is directed to a point 6.0 cm behind the lens, find the position of the image.
Solution
12.2 Converging and diverging lenses (SB p. 215)
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Solution:Solution:
lens. diverging thefrom cm 9.0 and real is image thepositive, is of value theSince
cm 096
1181111
111
v
.vufv
fvu
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TextText
12.2 Converging and diverging lenses (SB p. 215)
f = –18.0 cm (the lens is a diverging lens)u = – 6.0 cm (the point O is a virtual object)Using the lens formula,
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Q: Q: A thin converging lens of focal length 10 cm and a thin diverging lens of focal length 30 cm are placed in contact with each other.(a) Find the combined focal length.(b) Is the combination equivalent to a single converging or diverging lens?
Solution
12.2 Converging and diverging lenses (SB p. 216)
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Solution:Solution:
cm 15 301
101111
equation,length focal combined From (a)
21
ffff
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TextText
12.2 Converging and diverging lenses (SB p. 216)
(b) The combined focal length is positive, thus the combination is equivalent to a converging lens.
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Q: Q: An object is placed at a distance of 7.0 cm from a lens and a virtual image which is magnified eight times is produced.What are the focal length of the lens and the image distance?
Solution
12.2 Converging and diverging lenses (SB p. 218)
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Solution:Solution:
virtual.is image that theconfirms of valuenegative The :Note
cm 056 7.08
cm 08
17.08
1
11
8 :ionmagnificatlinear thereal, isobject theand virtualis image theSince
cm 7.0
v.v
uvm
.ff
fu
m
m
u
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TextText
12.2 Converging and diverging lenses (SB p. 218)
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Q: Q: A converging lens has a focal length of 20 cm. At what distance from the lens must an object be placed so that the linear magnification is of magnitude(a) 1, and (b) 4?
Solution
12.2 Converging and diverging lenses (SB p. 218)
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Solution:Solution:
.impossible is This 0
1201
1
1, Whencm 40
1201
1
11
1, When 1.or 1 then
1, is of magnitude theIf (a)
u
um
u
ufu
m
mmm
m
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TextText
12.2 Converging and diverging lenses (SB p. 218)
cm 15
1204
1
4, Whencm 25
1204
1
11
4, When 4.or 4 then
4, is of magnitude theIf (b)
u
um
u
ufu
m
mmm
m