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© Manhattan Press (H.K.) Ltd. 1

• 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


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)



Converging and diverging lenses

Converging lens

Diverging lens



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




principle focus (F)

principle focus (F)

focal length

focal length

Converging lens




Converging lens focal plane




Diverging lens

Focal length of diverging lens is -ve




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



Images in lenses

1. Ray diagram- used to determine position and nature of image

Ray 1



Images in lenses

Ray 2

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Images in lenses

Ray 3

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Images in lenses

2. Image formed by a converging lens

(a) Object at infinity

at principal focus; inverted, diminished, real image



Images in lenses


(b) Object distance u greater than 2f

f < v < 2f; inverted, diminished, real image



Images in lenses


(c) Object distance u = 2f

v = u = 2f; inverted, same size, real image



Images in lenses


(d) Object distance u between f and 2 f

v > u; inverted, magnified, real image



Images in lenses


(e) Object at principal focus (u = f)

at infinity; upright, magnified, virtual image



Images in lenses


(f) Object distance u less than f

upright, magnified, virtual image (as magnifying glass)



Images in lenses

3. Image formed by a diverging lens

upright, diminished, virtual image



Lens formula

Lens formula- used to determine image distance

fvu

ufuvvfvu

fvf

BIPAOPvu

PIPO

BIOA

fvf

BIOA

BIFQPFIFPF

BIPQ

111

)(

)(

lens formula



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.



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



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



Linear magnification

)(height Object )(height Image

)(ion magnificatLinear o

ihh

m

POPI

AOBI

hh

m o

i

uvm )(ion magnificatLinear



Linear magnification

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1

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:obtain we using and by t throughouformula lens eMutiply th 1.

111 formula, lens theFrom

:Note

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m

fu

vu

,uvmu

fvm

fv

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Example 6Example 6

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Example 7Example 7


End


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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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



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



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



Solution:Solution:

lens. thefrom cm 30 is image The

cm 30201

121111

111

vufv

fvu

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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



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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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,


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



Solution:Solution:

cm 15 301

101111

equation,length focal combined From (a)

21

ffff

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(b) The combined focal length is positive, thus the combination is equivalent to a converging lens.


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



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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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



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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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

1© manhattan press (h.k.) ltd. terms used for lenses images in lenses images in lenses 12.2...

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