Optical Instruments

Simple Microscope

The Structure of the Simple Microscope

Describe the structure of the simple microscope

A  magnifying  glass,  an  ordinary  double  convex  lens  with  a  short  focal  length,  is  a  simple

microscope.  The  reading  lens  and  hand  lens  ar e  instruments  of  this  type.  When  an  object  is

placed  nearer  such  a  lens  than  its  principal  focus,  i.e.,  within  its  focal  length,  an  image  is

produced that is erect and larger than the original object. The image is also virtual; i.e., it cannot

be projected on a screen as can a real image.

The Mode of Action of a Simple Microscope

Describe the mode of action of a simple microscope

The image  formed  by magnifying  glass or  simple microscope  is virtual and  erect  object place

between principal focus (f) and convex lens.

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The normal district vision

The position of the lens is usually adjusted so that V is about 25cm, which is the shortest

distance of distinct vision.

Using the equation of lens (Lens formula).

I/U + I/V = I/F

Adopting the 'real is positive' sign convention we obtain:

V = (-Ve) since the image is virtual.

I/U – I/V = I/F

V= 25 –(Normal district vision)

I/U – I/25 =I/F

I/U = I/F + I/25

(I/U)=-1 (25 + F )

25F

U = 25F/F+25

The above formula shows the means of obtaining the distance of object, U.

Magnication (

M)

of simple microscope

Magnification is the ratio of the image distance to the object distance.

M = Image distance, V

Object distance, U

Hence

M = v/u …………………..(i)

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From V = 25cm (distance of district vision)

From U = 25f/(f+25) ……………………… (ii)

Insert eqn (ii) into (i)

M = V/ (25f/(f+25)

M = 25/(25f/f+25)

M = 25/f + 1

Example 1

A simple microscope with lens of focal length 5cm is used to read division of a scale 0.5mm in

size. How large will the division be seen through the simple microscope?

Data given

Focal length, f = 5cm

Required to find magnification, M

Soln:

From

M = (25/f + 1)

= (25/5+1)

=(5+1)

= 6

The magnification of lens = 6

Let the size of the object be ho and that of the image be hi. Then:

M = h1/H ……………(i)

H1 = 6h

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The Height , h = (0.5mm)

H1 = 6 (0.5mm)

HI = 3mm

Hence, each division will appear to have a size of 3.0mm viewed through the simple microscope.

A Simple Microscope

Construct a simple microscope

Parts of simple microscope

Compound Microscope

The Structure of a Compound Microscope

Describe the structure of a compound microscope

A compound microscope  is an optical instrument used to produce much greater magnification

than that produced by simple microscope. The main features of a compound microscope includes

two short-focus convex lenses, the objective lens, and the eyepiece.

Demonstration

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The Mode of Action of a Compound Microscope

Describe the mode of action of a compound microscope

The  most  commonly  used  microscope  for  general  purposes  is  the  standard  compound

microscope. It magnifies the size of the object by a complex system of lens arrangement.

It has a series of two lenses; (i) the objective lens close to the object to be observed and (ii) the

ocular lens or eyepiece,  through  which the image is  viewed  by eye. Light  from a light  source

(mirror or electric lamp) passes through a thin transparent object.

The objective lens produces a magnified „real image  (first image of the object). This image is

again magnified by the ocular lens (eyepiece) to obtain a magnified „virtual image  (final image),

which can be seen by eye through the eyepiece. As light passes directly from the source to the

eye through the two lenses, the field of vision is brightly illuminated. That is why it is a bright-

field microscope.

The Magnification of a Compound Microscope

Determine the magnification of a compound microscope

The  object  lens  forms  a  real  and  inverted  image  I

of  the  object  O  (  the  image  is  slightly

I

magnified). The  eyepiece lens acts as a magnifying  glass for the first image II and produces  a

magnifical virtual image.

The object is placed just beyond the principal (fo) of the objective lens so that that the real image

I, is formed inside the principal focus (F) of the eye piece. The eyepiece treats the real image I,

as an object and then forms its magnified virtual image I2.

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Magnification of a compound microscope:

This isthe ratio of the image distance produced by a

compound microscope  to  the  object distance. The magnification produced by  objective lens  is

v/u.

Where

V is the image distance

U is the object distance

The magnification given by the eyepiece is given by;

Me = 25/fe + 1

If the final image is formed at the least distance of distinct vision (V = 25cm).

Mc = M

m

o

e

Combine eqn (i) and (ii)

Then

Mc = (v/u) (25/fe+1)

The above formula shows  that the final virtual image is formed at the least distance of distinct

vision.

Uses of a Compound Microscope

Mention uses of a compound microscope

The uses of a compound microscope includes the following:

Used to magnify microorganism such as bacteria which cannot be seen by naked eyes.

Used in hospitals widely to detect microor ganisms in specimens provided by patients. A

specimen  is  a  small  amount  that  is  taken  for  testing.  Blood  is  an  example  of  specimens.  In

hospitals  microscopes  can  detect  parasites  such  as  plasmodium  ssp  (a  causative  agent  for

malaria) in blood specimen.

Example 2

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A certain  microscope  consists of two  converging lenses of  focal length 10cm and 4cm for the

objective and eyepiece, respectively. The two lenses are separated  by  a distance of  30cm. The

instrument is focused so that the final image is at infinity. Calculate the position of the object and

the magnification of the objective lens.

For the objective lens

I/U + I/V = I/Fo

Where

Fo = 10cm

The objective lens forms a real image of the object at the principal focus of the eyepiece.

Thus

V = (30 – 4)

= 26cm

Thus I/U + I/V = I/10

I/U + 1/26 = 1/10

1/U = (1/10 – I/26)

(I/U) -1 = (4/65)

(1/U) -1 = (4/65)-1

U = (65/4)

The distance of object, U= 16.25cm

The magnification given by the objective lense is given by:

Whereas:

V = 26cm

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U= 16.25cm

Mo = (26cm/16.25cm)

The magnificent given by objective lens, Mo = 1.6.

Astronomical Telescope

The Structure of an Astronomical Telescope

Describe the structure of an astronomical telescope

An  Astronomical  Telescope  is  used  for  observing  heavenly  bodies  like  stars  and  planets

(generally bodies which are very far away from normal vision of human eyes ). Like compound

microscope, it consists of two convex lenses, objective lens and the eyepiece.

The  focal  length  Fb  of  the  objective  lens  is  longer  than  the  focal  length  Fe of  the  eye  piece

lens.Rays of light from a distant object are nearly parallel when they strike the objective lens of

the  Telescope.The  objective  lens  forms  a  real  image,  inverted  and  diminished  image  IQ  of  a

distant object is in the focal plane.The eye piece forms the final magnified image at infinity

When the telescope is adjusted in such a way that the final image is at infinity it is said to be in

normal adjustment.In this case the distance between objective lens and eyepiece is (Fb + Fe) This

is the maximum separation between the objective lens and the eyepiece lens.

The Mode of Action of an Astronomical Telescope

Describe the mode of action of an astronomical telescope

The main reason for a distant object to be smaller is that the two objects subtend different angles

at the eye. In other words, we can say that different angles substended by the eye causes a distant

object to appear smaller.

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The object AB and CD are of the Same height.The object CD is closer to the eye than AB.

The object  CD  appears  to  be  taller than  AB because  angle  B  that  CD  subtends  at  the  eye  is

greater than the angle x subtended by AB at the eye. Images there can be made to appear lar ge by

bringing them closer to the eye.

In a telescope the final image is magnified because it subtends a much gr eater angle at the eye

than does  a distant  object  observed without a telescope. B  is the angle  subtended by the  final

image at the eye and X is the angle subtended by a distant object.

The Magnification of an Astronomical Telescope

Determine the magnification of an astronomical telescope

The magnification of a telescope is defined as the ratio of the angel B (in radians) subtended by

the final image at the eye to the angle X subtended by a distant object at the eye.

Thus, for telescope the magnification is given by:

M = B/x ………………………………….i

From figure B= IQ/ID ……………………..ii

X = IQ/IA ………………………………………..iii

But Insert eqn (ii) and (iii) into eqn (i)

M = (12/ID)

(IQ/IA)

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M = (IA/ID)

But IA = fo and IF =fe

M = fo/fe……………………………….(x)

Where

Example 3

fois the focal length of two thin converging lenses of focal lengths 25cm and 4cm respectively. It

is focused on the moon which subtends an angle of 0.6° at the objective lens. The final image is

formed at the observers least distance of distinct vision (25cm in front of the eyepiece). Find the

diameter of this image.

In the previous figure:

X = h/fo

Where fo is the focal length of the objective lens

X = h/25

Where X is the angle in radians subtended at the objective lens by the moon.

H = 25x

H = 25 (6/10 x 11/180)

H = 25 (6/10 x 22/7 x 1/80)

H = 0.2619m

The height of the image, h = 0.2619m

The distance of this image from the eyepiece is obtained from the relation:

I/U + I/V = I/fe = 4cm

V= -25cmV = -25cm

I/U – I/25 = ¼

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I/U = (1/4 + 1/25)

(I/U)-1 = (25 +4) -1/100

100U= (100/29)

The magnification, m of the lens:

M = V/u

M = (25CM/100/29)

M = 29/4

Let the height of the final image of the moon be h:

M = Hi/h

hI = mh

HI = (29/4) (0.2619)

HI= 1.90cm

The Height of image Hi = 1.9cm

Hence

The diameter of the final image of the moon will be 1.90cm

Observation of the universe today are best made from the Hubble Telescope. Outside the Earth s

atmosphere, this telescope suffer from less inter ference.

Uses of an Astronomical Telescope

Mention uses of an astronomical telescope

Astronomers use telescopes because they're much better than our eyes. Here are a few reasons:

1.

Telescopes see lots of  colours - telescopes  can collect  light that our eyes are unable to:

radio, microwave, infrared, ultraviolet, x-rays and gamma rays.

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2.

Telescopes collect lots of light - our pupils are only a few millimeters across, so we can

only collect photons over a tiny area whereas telescopes can collect photons of huge areas (e.g. a

football fields worth for radio telescopes).

3.

Telescopes see fine details because of the wave nature of light and the nerves in our eyes,

we can only see details about the same angular size as Jupiter's width. Telescopes can allow us to

resolve fine details - like Jupiter's Great Red Spot.

4.

Telescopes can record observations with camer as - You can see things with your eye and

draw them, but telescopes can share observations with the world! This is especially important for

convincing skeptics that what you saw was real!

A Simple Astronomical Telescope

Construct a simple astronomical telescope

A simple telescope

Projection Lantern

The Structure of the Projection Lantern

Describe the structure of the projection lantern

The projection lantern forms images of slides or camer a film onto a distant screen. The film or

slide to be projected is inverted and highly illuminated.

The Mode of Action of a Projection Lantern

Describe the mode of action of a projection lantern

Optical arrangement of projection lantern.

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The slice or film to be projected is inverted and highly illuminated.

The  concave  mirror  helps  to  concentrate  the  light  which  would  otherwise  be  partly

wasted.

The lamp is placed at the principal focus of the concave mirror.

The heat filter reduces the heat at falling on the slide or film so as to avoid it overheating.

Since the image of the projection lantern is Highly magnified, it would not be very bright

if there was not enough illumination.

The  condenser  directs  a  maximum  amount  of  light  from  the  source  of  the  slide  and

produce uniform illumination the screen. (The condenser is a double in order to reduce chromatic

aberration).

The projection lens forms the image of the slide on the screen.

The light source is usually located at a distance of 2f from a condenser and invited so that

the image on the screen is upright (erect).

The focal length  of the projection lens is  ABOUT TWICE  THE  FOCAL length  of the

condenser since the screen is usually far from the lens.

The Magnification of a Projection Lantern

Determine the magnification of a projection lantern

Example 4

A lantern projector  using a slide of (2cm x 2cm) projects a picture  (1cm x  1cm) onto a screen

12m  from the projection lens. How  far from the lens  must the slide be? Find  the  approximate

focal length of the projection lens.

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Solution

The magnification m is given by;

M = V/U ………………………………………i

Where

H

I

is the size of image

H is the size of object

U object distance

V image distance

Thus

M = Hi …………………. ii

Then eqn (i) = eqn ii

v/u =hi/h

(1200/u)-1 = (100/2) -1

(u/1200) = (2/100)

U = (2/100) (1200)

U = 24cm

The object distance, U = 24cm

Uses of a Projection Lantern

Mention uses of a projection lantern

Projection lantern are used in various areas. These include:

Projection of films, slides and transparencies,

projection of opaque objects, i.e. episcopic projection,

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used in searchlights and headlights,

used in projection apparatus in industry for gauge and screw thread testing,

used in physical experiments such as projection of a spectrum,

used in polarisation experiments and interference experiments.

A Simple Projection Lantern

Construct a simple projection lantern

Projection Lantern

The Lense Camera

The Structure of the Lens Camera

Describe the structure of the lens camera

Lens camera is an instrument which produces an image of object on the screen using light. The

basic  physical  principle  of  all  camera  is  the  same  in  spite  of  the  variation  in  the  design  of

cameras.

The optical system  of the camera are very  similar  to that  of the lantern projector  but with the

direction  of  light  r eversed.The  converging  lens  forms  a  real  image  of  the  object  to  be

photographed.(This image is diminished (smaller than the object and inverted)

The  lens  can  be  moved  back  and  forward  with  the  help  of  focusing  any  so  that  objects  at

different distances can be brought to the focus.A forced image is locate on the film or plate when

the shuttled is open for a suitable amount of time as determined by the shutter speed.

Light enters the camera Box and makes a picture of the object on the film “( The film is sensitive

to light)

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The camera is equipped  with a diagram or  light entering  the  camera.It ensures that  is incident

centrally on the lens so that the distortion of the image formed is reduced

The Mode of Action of the Lens Camera

Describe the mode of action of the lens camera

The aperture stop, which is the limiting diameter of the aperture thought which light  enters the

camera (given as fraction of focal length F of lens) is also called F Number.

This  F  Number;  is the fraction of  focal length of the  lens given as focal  length divide by lens

diameter.

F number = Focal length, F/Lens diameter, d

FN = F/d

Where d = is lens diameter.

The Number Indicates the Number of times the focal length F of times the focal length F

of the lens diameter ( or stop)

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The smaller the F - Number for a given focal length the larger the lens diameter

The lens with a larger diameter has a greater light- gathering power or speed

This for such a lens the shutter allows light in the camera for a short interval of time.

The Magnification of the Lens Camera

Determine the magnification of the lens camera

Magnification  of  a  lens  camerais  obtained  as  the  ratio  of  the  Image  distance  and  the  object

distance.

But from the lens formula:

Thus M = v/U

I/U + I/V = I/F

I/V = I/F - I/U

(I/V)

–I

= ( U - F / FU)

-I

V = FU/ ( U - F)

Example 5

A lens camera is to be used to take a picture of a man 2m tall if the  lens of the camera  Has a

focal length of 10cm, calculate the minimum size of the film frame required, given that the man

is 20.1m from the camera.

Solution:

Magnification is given by:

M = f/ (u-f)

Where

F= 10cm U = 201/m / 2010cm

M = ( 10/2010 – 10)

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M = 1/20 ....................................i

Let the size of the frame be h when the height of man is 2m.

Then

M = 1/200

But h1/h = 1/200

h1 = (1/200) 2

h1 = (1/200)2

h1 (2/200)

h1 = (1/100) m

h1 = 1cm or 10mm

The film frame should be at least 10mm square.

Simple Lens Camera

Construct a simple lens camera

A simple lens camera

The Human Eye

The Structure of the Human Eye

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Describe the structure of the human eye

The eyeball approximately spherical in shape.The wall of this sphere consist of two  layers, the

outer layer or sclera and the inner layer or choroid.The front portion of the SCLERA FORMS A

TRANSPARENT CURVED  section called the camera.The  choroid  layer is balance  in order  to

prevent internal reflection and also to protect the light sensitive parts of the eye.

The  aqueous  and  vitreous  hum  our  are  jelly  –  like  substance  that  fills  the  spaces  within  the

eyeball.The aqueous humour is the salt solution of refractive index n, 1.38.Vitrous hurmour is a

watery , Jelly  substance  of refractive index  1.34.Behind  the  cornea there  is a  colored diagram

called the iris.

The iris has the central hole called the pupil. The iris contains muscles which control the size of

the pupil. The size of the pupil decreased in the bright light and increased in the dim light.

Behind the pupil and there is a crystalline lens held in position by suspensory ligaments that are

attached to the choroid layer.Near the suspensory ligaments are the ciliary muscles.The function

of the suspensor ligaments there are the cilliary muscles.

The function  of cillary  muscles  is to control  the  thickness of  the  lens.  The  lens  become  thick

when the ciliary muscles contract and thin when the ciliary muscles are relaxed.

At  the  back  of  the  eye  there  is  a  retina  (This  is  the  part  of  the  eye  which  is  sensitive  to

light).Image  formed  is  inverted  formed  on  the  Retina  (  This  is  the  part  of  the  eye  which  is

sensitive to light.)

Image formed is inverted formed on the retina by successive refraction of light at the corner, the

aqueous  hurmour  the  crystalline  lens  and  the  Vitreous  hurmour.Electrical  signals  are  then

transmitted to the Brain through the topic nerve. Finally, the brain interprets these signals.

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Accommodation Power of the Human Eye

Explain accommodation power of the human eye

Accommodation is the process whereby the eye alters its focal length in order to form images of

objects at different distances.

(Thickening or Thinning of the lens causes a change in its focal length).

The thickening or thinning  of the cr ystalline  lens is  made possible  by the action  of the ciliary

muscles.To view neare object t, ciliuary muscles contract, this makes the lens thicker.

In the relaxed state of ciliary muscles, the cr ystalline lens become thinner and enables the eye to

see (view) distant objects. The farthest point which can be seen clearly is called the far point of

the eye and the nearest point is called the near point of the eye.

The corresponding distance from these points to the eye are referred to as the maximum and least

distance  of  district  vision respectively.A  normal  eye  (i.e.  without  defects  of  vision)  has  a far

point at infinity and near point at a distance of 25cm from the eye.Structure of lens “ view distant

object”

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The Defects of the Human Eye

Identify the defects of the human eye

Myopia or near-sightedness

This  defect  causes  person  to  see  near  object  clearly  while distant  objects  are  not seen

clearly.

The strength of the cornea and the eye lens combination is too great even when muscles

of the eye are completely relaxed.

The focal  length of  the cornea  and  the eye – lens combination  is  always less  than the

distance to the retina.

Images of distant object are formed in front of the retina even when eye is totally relaxed.

However, an object that is closer can be brought into focus.

In this situation  the focal length  of the cornea  and the eye lens is  so  short that  objects

closer  than  the conventional  (near point  of 25cm)  can  be  brought  into  focus.  That  s why  this

condition is called Short sightedness (near sightedness).

Since the problem is that the strength of the eye – lens and the cornea combination is too

great, the solution is to provide eye glasses (or contract lenses) with negative lens.

The negative lens weakens the strength of the cornea and eye – lens just enough so that

the resulting  focal  length  when the  eye  muscles  are  relaxed  matches  the  distance  back  to  the

retina so that distant images are now in focused.

The eye glass lenses are negative lenses that means they are thinner in the middle than at

the edges.

It is easy to identify this kind of eye glass lenses since acting by themselves they do not

form a real image of an object at any distance.

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Hyperopia or far-sightedness

This defect causes a person to see distant objects only and short-distance objects are not

seen clearly.

In the person with this condition, the strength of the cornea and the eye-lens combination

is too weak when the eye muscles are totally relaxed. So the image of a distant object is formed

behind the retina.

The solution in the opposite of myopia. Victims should wear positive eye lenses which

strengthen the corner and the eye lens just enough so that the resulting focal length when the eye

is relaxed matches the distance to the back of the retina.

Astigmatism

This occurs when the focal length for the cornea and the eye's lens for an object oriented

in some direction is not the same as for another located in a perpendicular direction.

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The eye can not bring the vertical and horizontal lines in a „+  symbol in sharp focus at

the same time. (The axis of differing focal length need not be exactly horizontal and vertical).

The problem is that the cornea of the eye lens is not symmetrical. The solution is to use

eye glasses whose lenses are not symmetrical in a complementary way.

The cylindrical lens may be combined with an additional positive or negative lenses.

Decreased accommodation

This condition typically occurs in middle-aged people.

The  eye  muscles  gradually  weaken  with  age,  so  that  the  range  or  accommodation  is

decreased.

People with this condition cannot bring both near objects and far objects into focus.

The  weakening  of  the  eye  muscles  often  causes  the  focal  length  of  the  eye  lens  to

increase as well so that many people of middle age tend to become far sighted.

Since the problem is adequate accommodation,  no single  lens can correct it and people

with this problem usual needs bifocals.

Bifocals  are  glasses with two  different  lens  strengths,  one for  near and one for  distant

objects.

The usual arrangement is that the bottom half of the lens is the near strength and the top

half is the far strength.

The Correction of the Defects of Human Eye

Describe the correction of the defects of human eye

Myopia

is common name for impaired vision in which a person sees near objects clearly while

distant objects appear blurred. In such a defective eye, the image of a distantobject is formed in

front of  the retina and not at the retina itself. Consequently, a nearsighted person cannot  focus

clearly on an object farther away thanthe far point for the defective eye.

This defect arises because the power of the eye is too great due to the decrease in focal length of

the crystalline lens. This may arise due to either

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1.

excessive curvature of the cornea, or

2.

elongation of the eyeball.

Correction:

This

defect

can  be

corrected

by  using  a

concave  (diverging

)  lens.  A  concave  lens  of

appropriate power or focal length is able to bring the image of the object back on the retina itself.

Farsightedness

,  also  called  hypermetropia,  common  name  for  a  defect  in  vision  in  which  a

person sees near objects with blurred vision, while distant objects appear in sharp focus. In this

case, the image is formed behind the retina.

This defect arises because either

1.

the focal length of the eyelens is too great, or

2.

the eyeball becomes too short, so that light rays from the nearby object, say at point N,

cannot be brought to focus on the retina to give a distinct image.

Correction:

This defect can be corrected by using a

convex

(

converging

) l

ens

of appropriate focal

length.  When  the  object  is  at  N ,  the  eye  exerts  its  maximum  power  of  accommodation.

Eyeglasses with converginglenses supply  the  additional focussing  power  required for  forming

the image on the retina.

The Human Eye and the Lens Camera

Compare the human eye and the lens camera

The camera

1.

The eye and the camera has a have a convex lens which form a real and inverted image of

an object.

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2.

The eye and the camera are blackened inside to prevent internal reflection. Rays of light

which are not received on the retina or camera film are absorbed by the choroid layer of the eye

or the black surface inside the camera.

3.

The eye can regulate the amount of light that passes through the crystalline lens by using

pupil while in a camera the diaphragm r egulates light.

4.

In the eye the image is formed in the retina while in the camera the image is formed on

the photographic plate.

5.

The eye  can change the focal length of its lens by the contraction and relaxation of the

ciliary muscles. In this way the eye can focus objects at different distance. In a camera objects at

different distance are focused on by moving the lens forwards and backwards.

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