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LECTURE NOTES PHYSICS STEPS A TCY Program _______________________________________________________________________________________

STEPS____________________________________________________________G e t f r e e c h a p t e r w i s e t e s t s f o r C l a s s X

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w w w . t c y o n l i n e . c o m

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NATURE OF LIGHT & REFLECTIONProperties of Light:

Under normal circumstances - i.e. traveling through a uniform medium, light travels in a

straight line. Such traces along the path of light are called rays. A bunch of raysconstitute abeam of light.

1. However, the following phenomena can alter the path or nature of the light.

(a) Absorption

Light falling on an object may be absorbed, transmitted, or reflected.

(b) Reflection

Those surfaces which reflect the most light appear white, or silver. A highly polished,

smooth and flat silver surface acts as a mirror, reflecting a perfect image of the world

around it.

(c) Refraction

Light that is transmitted through a medium will usually be deviated somewhat from

the straight path it was previously following.

Refraction is an important characteristic of lenses that allows them to focus a beam

of light onto a single point. Refraction occurs as light passes from a one medium to

another when there is a difference in the optical densitybetween the two materials.

2. Wave/Particle Duality

Light may be regarded as a flood of particles, called photons, or as a wave. In either

case, it carries energy through a vacuum at a velocity which is a universal physical

constant, and is the same for all observers and for all colors.

Light frequently behaves as a particle.

3. Speed of light.

The speed of light in vacuum is a universal constant (3 x 10 8 m s-1). It is the same

for all frequencies of light. The colour of light depends on the frequency of light.

Different colours of light travel with different speeds in all other mediums except

vacuum. The wavelength of visible light lies in the range of 4m - 7m.

The Reflection of Light:

Incident Ray: A ray of light falling on a reflecting surface is called incident ray.

Reflected ray: A ray of light reflected by the reflecting surface is called reflected ray.


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Point of Incidence: It is a point on the reflecting surface where a reflected ray and

incident ray meet.

Normal: A perpendicular drawn on reflecting surface at the point of incidence is

called normal.

Incident angle: The angle drawn in between incident ray and normal.

Reflected angle: The angle drawn in between reflected ray and normal

Laws of reflection:

Angle of incidence = angle of reflection

The incident ray, reflected ray and Normal are coplanar.

Image: A point where an object appears to be, because the rays from any given point on

the object have been bent so that they come back together and then spread out again

from the image point, or spread apart as if they had originated from the image

Real image: A point where an object appears to be, because the rays from any given pointon the object have been bent so that they come back together and then spread out again

from the new point.

Virtual Image: A point where an point object appears to be, because the rays from any

given point on the object have been bent so that they spread apart as if they had

originated from the point.

An extended object contains many points and the image of the extended object contains

the images (real or virtual) of all the object points.

Plane mirror: Consider an object placed a certain distance in front of a mirror, as shown

in the diagram.

Here it is obvious that h0 = hi (distance between parallel lines) (i)ACB = BCX = (Laws of reflection) (ii)

ECD = BCX = (Vert. opp. angles) (iii)

tan = h0/do = hi/di

hence di = do (From (i), (ii) & (iii)

X


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Image characteristics - Plane mirrors: Images formed by plane mirrors are

virtual (for real object)

upright

left-right reversed

the same distance from the mirror as the object's distance, and

the same size as the object.

Lateral Inversion: The exchange of right and left side of an object and its image is called

lateral inversion.

Spherical mirrors:

A spherical mirror is one whose reflecting surface is a part of a hollow sphere. The

spherical mirrors are of two types : concave mirror and convex mirror.

Concave mirror: is silvered from outer side and the reflection takes place at the

inner (concave) surface.

Convex mirror: is silvered from inner side and the reflection takes place from outer(convex) surface.

SPHERICAL MIRRORS DEFINITIONS

Center of curvature (C): is the center of the sphere whose curvature would be identical to

that of the mirror; therefore the center of curvature would be at the center of the sphere

that the mirror would form if the mirror curved all the way around.

Focal point (f): The point through which all light rays coming into the mirror parallel to

the axis would reflect through, or appear to have reflected from.

The mirror (principal) axis: The line which passes through the pole (vertex), the center of

curvature, and the focal point. It is normal to the mirror at its pole (vertex).

Pole (vertex): The physical center of the mirror surface.

Aperture: The width of the reflecting surface is called aperture.

Focal length: The distance of separation between the pole and the focus is called focal

length.


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Rules for drawing ray diagrams:

Light incident parallel to the axis will be reflected through the focal point.

The reverse of this is true, also. Light passing through the focal point will be

reflected parallel to the axis.

Finally, light striking the vertex will be reflected at an equal angle to the axis.

RAY DIAGRAM FOR CONCAVE MIRROR

(i) Position of object at :

Nature of the image: Image is real point sized at focus.

(ii) Position of object; Beyond C

FC

F C

F

F


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Nature of image: Image is inverted, small and in between C and F.

(iii) Position of object at C

Nature of image: Image is inverted, same sized at C

(iv) Position of object in between C and F

Nature of image: Large in size, inverted, beyond C

(v) Position of object; At F

Nature of image: Image is at infinity. Highly enlarged and real


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(vi) Position of object; In between P and F

Nature of image: Image is virtual, erect and enlarged

CONVEX MIRRORS

Object at infinity parallel rays converge at the principal focus:

All other cases: Image formed is virtual, upright and reduced in size

New Cartesian Sign Convention:

The object will always be placed on the left of the mirror/lens

Distances measured along principal axis is measured from pole

Distance measured along the direction of the incident ray is positive and opposite to

it is negative.

Heights measure upwards from principal axis is positive and downward relative to

principal axis is negative.

F C


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THE MIRROR FORMULA

Assumptions for mirror formula

(a) The rays are close to the principal axis.

(b) The aperture of the mirror is small.

Applying Cartesian sign conventions

image distance = v

object distance = u

focal length = f

height of object = ho

height of image = hi

from assumption (a) arc MON can be approximated as a straight line.

Then from 1 and 2

tan =)f(u

ho

from 1

tan =f

hi from 2

Combing we getuf

ho

=

f

hi o

i

h

h=

fu

f

(i)

tan =f

ho from 3 tan =)f(v

hi

from 4

fv

hi

=f

ho

o

i

h

h=

f

fv (ii)

From (i) & (ii)

fu

f

=

f

fv

f2 = (u f) (v f) f2 = uv fv fu + f2

uv = fv + fu

dividing throughout by uvf

v

1

u

1

f

1+=

ho

-u

-v

-f

hi

ho

M

O

hiN

(2)

(3)

(4)

(1)


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Magnification (m): It is defined as the ratio of the size of the image (h2) to the size of the

object (h1)

M =)ho(objectofsize

)h(imageofsize i

For a concave mirrorfis positive. For a convex mirror,fis negative.

M = u

Some important Points:

(i) Positive magnification means both the object and image are upright (i.e., erect)

(ii) Negative magnification means, object and image have different orientations. If object

is upright (i.e., erect), then image is inverted (i.e., in the downward direction with

respect to the principal axis).

USES OF CONCAVE AND CONVEX MIRROR

Concave mirror is used

(i) as a reflector to concentrate light

(ii) as shaving mirror

(iii) in ophthalmoscope to examine throat and ear of a person generally, parabolic

(concave) mirrors are used.

(iv) as a reflecting type astronomical telescope

(v) in search light, head light of automobiles etc.

Convex mirror are used

(i) in automobile to see large traffic at the back.

(ii) as a device to check theft in shops

(iii) to view the corners which are not directly reachable.


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REFRACTION OF LIGHTLaws of refraction of light:

(i) The incident ray, the refracted ray and the normal are co-planar.

(ii) A ray of light traveling along the normal will not get refracted and will pass un-

deviated.

(iii) The ratio of the sine of the angle of incidence to that of the sine of the angle of

refraction is constant for a given pair of media. This constant is called the refractive

index n. This is called the Snells Law.

Thus Snells Law gives

Sin i = n Sin r

Rules of refraction:

When a light ray travels from a rarer medium to a denser medium, the light ray

bends towards the normal When a light ray travels from a denser medium to a rarer medium, the light ray

bends away from the normal.

Note:As the speed of light is reduced in the slower medium, the wavelength is shortened

proportionately. The frequency is unchanged; it is a characteristic of the source of the light

and unaffected by medium changes

Optical Density: Consider two transparent media, A and B. If light travels more slowly in

medium B than in medium A, we say that medium B is more (optically) dense than

medium A.

Refractive Index: The refractive index for light passing from medium 1 to medium 2

(written n21) is given by

n21 =2

1

v

v

2mediuminlightofvelocity

1mediuminlightofvelocity=

If we consider light passing from a vacuum (or air) to a medium the ratio of the velocities

is called the absolute refractive index ofthe medium. The velocity of light in a vacuum

(or air) is c.


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In the diagram above

n2 =2

v

cn1 =

1v

c

so the relative refractive index of light passing from medium 1 to medium 2 is given by

n21 =

1

2

n

n

n1sin1 = n2sinn2

(n21 means I of med. 2 w.r.t. 1

It should also be clear that n21 = (n12)1

n32 = n31 n12 =21

31

n

n

Lens: A transparent optical device used to converge or diverge transmitted light to form

an image

Convex lens: A lens that is curved outward (convex): the ends are narrow and the middle

is wide. Often referred to as a converging lens. A convex lens can produce either a real or

virtual image. They are used to correct hypermetropia.

Concave lens: A lens with inward-curving (concave) surfaces: the ends are wide, the

middle is thin. Light passing through a concave lens is diverged. Concave lenses can be

used in telescopes, microscopes, and eyeglasses. In glasses, they are used to compensate

for myopia (nearsightedness).It always produces virtual images.

Uses of lenses: One important use of lenses is as a prosthetic for the correction of visual

impairments such as myopia, Hypermetropia, presbyopia, and astigmatism.

Another use is in imaging systems such as a monocular, binoculars, telescope,

telescopic gun sight, theodolite, microscope, and camera (photographic lens).

A single convex lens mounted in a frame with a handle or stand is a magnifying

glass.

Radio astronomy and radar systems often use dielectric lenses, commonly called a

lens antenna to refract electromagnetic radiation into a collector antenna.

RAY DIAGRAMS FOR LENSES

A ray passing through the optical centre of the lens: This ray is not deviated (this is

true for both convex and concave lenses)


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A ray parallel to the principal axis: For a convex lens (also called a converging lens),

this ray is deviated to pass through the principal focus, F.

For a concave lens (also called a diverging lens), this ray is deviated so as to appear to be

coming from the principal focus, F.

When drawing ray diagram for lenses, for simplicity we imagine that the refraction takes

place at the centre of the lens. In reality, of course, the light changes direction at the

surfaces.

RAY TRACING

Convex lens:

For an object outside the focal point, a real inverted image will be formed


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For an object inside the focal point, a virtual erect image will be formed

Convex lens:

The ray diagrams for concave lenses inside and outside the focal point give similar results:

an erect virtual image smaller than the object. The image is always formed inside the focal

length of the lens.

The Lens Equation:

tan = h/-u = H/v

H/h = -v/u

The ratio H/h is called the linear magnification produced by the lens.

Now,

tan = h/f=H/(v-f) orf

fv

h

H =


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This givesf

fv

u

v =

which, after a bit of rearrangement gives 1/v 1/u = 1/f

This is called the lens equation.

Power of a Lens:The power of a lens is defined

P (D) =)m(f

1

Where f is the focal length (in metres) and the power is measured in diopters, or m-1.

Power of a converging lens is positive and of a diverging lens is negative.

Critical angle: The critical angle can be defined as the maximum angle of incidence

possible in denser medium for the ray to just emerge out into rarer medium. When angle

of incidence exceeds critical angle Total Internal Reflection occurs.

Total Internal Reflection: Total internal reflection is an optical phenomenon which

occurs when light propagating in a dense medium (such as glass) moves into a less dense

medium, such as water. When angle of incidence exceeds critical angle refraction stops

and reflection takes place.

TIR only takes place when both of the following two conditions are met:

the light is in the more dense medium and approaching the less dense medium.

the angle of incidence is greater than the so-called critical angle.

TIR finds use in esign of optical fibres, periscopes, binoculars, projection lanterns, reflex

camera and jewellery cutting and polishing.

Stars Twinkle While Planets Dont: Stars appear as point objects in the night sky due to

their large distance from earth. Moving pockets of air (having different optical densities) in

the Earth's atmosphere distort the light from these stars. These pockets of air refract light

in random directions before some of the light reach our eye. Hence the apparent position

of star fluctuates producing the twinkling effect.


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Planets don't appear to twinkle because they are much nearer to Earth than stars. Rather

than being points of light, planets are small discs. As their light is more spread out, even

if some of it is absorbed by our atmosphere, some of the light still filters through, so the

planet doesn't twinkle.

Other related effects of atmospheric refraction: Sun is visible to us 2 minutes before

actual sunrise and 2 minutes after actual sunset.

The sun appears to be flattened at sunrise and sunset.

Mirage:

An optical mirage is an image of an object that appears to be in a location other

than the correct one, as the result of abnormal atmospheric conditions. Heat

radiating from a hot earth surface, such as a desert, causes a reduction in air density just

above the surface. Hence the density of the air increases from bottom to top continuously.

The boundaries between the hotter and colder layers bend light rays from a distant object

continuously. After some time the rays undergo total internal reflection and when the rays

finally enter the observers eyes as shown in figure the image produced by the rays

appears inverted and below the real object. Just as an image reflected in water appears

when observed from a distance. This is very common on a paved road in hot weather.

Such reflections are known as inferior mirages.

In the case of a mirage at sea, the denser layers of air are next to the cool surface of the

water, and the reflection takes place from the rarer atmosphere above. Thus the object

appears distorted, elongated, and suspended in the air, producing a so-called looming

effect. Mirages which cause objects to be seen over the horizon are so called superiormirages


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R

O

Y

G

B

I

V

OPTICS OF COLORS & OPTICALINSTRUMENTS

Dispersion of white light: In optics,dispersion is a phenomenon that causes the

separation of a wave into its components with

different frequencies, due to a dependence of

the wave's speed on its frequency

Dispersive prisms are used to break up light

into its constituent spectral colours because

the refractive index depends on frequency

the white light entering the prism is a mixture

of different frequencies, each of which gets bent slightly differently. Refractive index n

decreases with increasing wavelength (or decreasing frequency). Thus, blue light, witha higher refractive index, will be bent more strongly than red light, resulting in the well-

known rainbow pattern.

COLORS OF OBJECTS

Primary Spectral Color: A primary color is a color that cannot be created by mixing

other colors. Additive primary colours are red, green, and blue. Additive mixing of red

and green light, produce shades of yellow or orange. Mixing green and blue produces

shades of cyan, and mixing red and blue produces shades of purple and magenta. Mixingequal proportions of the additive primaries results in shades of grey; when all three colors

are fully saturated, the result is white.

Composite Color: Mixing two primary colors produces what is generally called a

composite color. Composite colors are also obtained by subtracting a primary color from

white light.

Complementary colors: Two colors are called complementary if, when mixed in an

additive system, they produce a shade of white

Applications:TV works on the principle that mixing primary colors in various proportion

gives us the entire spectrum of colors. Painters use primary colors of paint to form

different color combinations.

Subtractive colors: Subtractive color explains the theory of mixing paints, dyes, inks,

and natural colorants to create colors which absorb some wavelengths of light and reflect


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others. The color that an object appears to have is based on what parts of the

electromagnetic spectrum are reflected by it, or conversely by what parts of the spectrum

are not absorbed. Anything that is not additive color is subtractive color. No other color

mixing systems are known. In color printing, the primary inks used are cyan, magenta,

and yellow. Cyan is the opposite of red, meaning that cyan acts like a filter that absorbs

red. The amount of cyan applied to a paper will control how much red will show. Magenta

is the opposite of green, and yellow the opposite of blue. With this knowledge an infinite

number of color combinations are possible. The color subtracted from white light is said

to be supplementary to the color that the pigment reflects.

OPTICAL INSTRUMENTS

The Eye: We are able to see things because light waves bounce off from objects into our

eye. When the light reaches our eyes several things happen.

Light rays pass through a transparent part of the eye called the cornea. The cornea is

curved and bends light inward. The light is bent even further as it passes through a liquidbehind the corena.

Next, light reaches the black

opening in the middle of the

coloured part of each eye. This

part of the eye is called the

pupil. The coloured part is

called the iris, and it makes

the pupil change size

depending on the different

amounts of light. For example

when the light is bright, the

iris makes the pupil small.

Once light passes through the pupil, the light enters a part of each eye known as the lens.

Ciliary Muscles on the sides of the lens change its shape so it can alter the focal length of

the lens and focus the rays on the retina. This is called accomodation

After the light passes through the lens the light is bent still further. This bending takes

place in a jelly like matter inside each eye called vitreous humour. This is also what

helps your eyes to keep their shape.

Finally the light forms an image on part of the inside wall of each eye. This wall is called

the retina and is made up of millions of special cells. These cells send message about the

image to your brain.

There are two types of Light sensitive cells on the retina. Rods, are sensitive to intensity

of light, and are concentrated on the sides of the retina. Cones are used for color vision,

and are concentrated in the center of the retina. Vision is most acute in the area of the

retina known as the fovea centralis.


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These messages travel along a nerve called the optic nerve. The point where optical

nerves enter the retina is called the blind spot which due to absence of rod cells cannot

sense images formed on it.

Notes:

Least Distance of distinct vision (D): The closest distance that the 'normal' human eye

can observe clearly; without any strain to the eye is called the least distance of distinct

vision. It is also called near point.

In connection with optical instruments the object would be considered to be held

whenever feasible at the least distance of distinct vision for determining its apparent size

even if the actual position of the object may not be at (D). Usually D = 25 cm.

Far Point:The far point of the eye is the location of the farthest object on which the fully

relaxed eye can focus.

Persistence of vision: The retina captures and holds an image for one-sixteenth of a

second before processing the next image. If images are flashed before the eye at least 16frames per second, the brain thinks it is seeing a single moving image. This is also the

principle of cinematography. In modern motion pictures 24 or more frames per second are

used.

Power of accommodation: Power of accommodation is the maximum variation in the

power of eyes while focusing on near and far object. The value of power of accommodation

for normal vision in young adult human being is approx. 4 D

EYE PROBLEMS

Presbyopia: Accommodation is the process by which the lens changes shape to allow the

eye to focus at different distances. With age, accommodation becomes more difficult.

This is called presbyopia. Hence the person develops problem of nearsightedness and far

sightedness simultaneously. Bifocal lens are used to correct this defect.

Myopia:

Excess refractivepower focuses rays

before they reachthe retina.

Nearsightednesscorrected by anegative lens toreduce refractive

power.


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Nearsightedness may be caused by various things. For instance, genetically, a persons

eyeball may be to long, causing the rays to focus too far in front of the retina.

Nearsightedness, or myopia, is when the Light rays converge too far in front of the retina.

Corrective lenses for myopia are diverging lenses. The diverging lens will cause the Light

rays to bend outwards enough, so that when the rays hit the lens of your eye, they will be

far enough apart to focus correctly onto the retina.

Hypermetropia:

On the other hand, farsightedness can be caused by a persons eyeball being too short,

which will cause the rays to focus in back of the retina. Converging lenses are needed to

correct hypermetropia. The converging lens will cause the rays to come in enough before

they hit the lens, so that they will focus onto the retina properly. Oftentimes,

hypermetropia is latent, or hidden, because the eye can accommodate enough to make up

for the hypermetropia.

Astigmatism: Another error that the eye can have is astigmatism. An irregularly shaped

cornea or lens will cause astigmatism. It makes objects appear to tilt. Cylindrical lenses

are needed to correct astigmatism. The cylindrical lens causes certain Light rays to bend

more than others. This will counteract the irregularities of your cornea or lens

Cataracts: When the inner lens of the eye becomes darkened or opaque, the condition is

called a cataract. The lens may be surgically replaced with a plastic lens.

Insufficient refractivepower to focus rayson retina.

Farsightedness corrected by a positive lens to addrefractive power.


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Final image at infinity Final image at near point

OPTICAL INSTRUMENTS

Resolution of an Optical Instrument: Resolution is the smallest separation for which

two closely-spaced points are distinguishable.

Essential components in the design of optical instruments

Resolution Magnification

Simple Microscope:

The simple magnifier achieves angular magnification by permitting the placement of the

object closer to the eye than the eye could normally focus.

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

simple microscope. The reading lens and hand lens are 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.. its magnification is

limited to 10.

M =f

D

This represents a lower magnification than when the image is at the near pointbecause

D is a negative quantity (it is a virtual image distance).

This real image is then viewed through the eyepiece which acts as a simple magnifier to

further enlarge the image.

Compound microscope: A compound microscope uses a very short focal length objective

lens to form a greatly enlarged image. This image is then viewed with a short focal length

eyepiece (ocular) used as a simple magnifier. The image should be formed at infinity to

minimize eyestrain.


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Note:Though both the eyepiece and objective have short focal length to keep the instrument

compact, comparatively the eyepiece is of large aperture as well as focal length.

The objective forms a real and inverted image between the two lenses. The eyepiece is

adjusted so that this image just falls within its focus. So this image would act as the

object for eyepiece and a final virtual magnified image is obtained by the eyepiece. This

image is inverted with respect to the original object.

The general assumption is that the length of the tube L is large compared to either fo or fe

so that the following relationships hold.

The linear magnification provided by the objective lens is

Mo = -L/fo

The eyepiece acts as a simple magnifier, so its magnification isMe = D/fe

The total magnification of a microscope is

M = Mo Me= -L.D/ fo.fe

The Astronomical Telescope: The astronomical telescope makes use of two positive

lenses: the objective, which forms the image of a distant object at its focal length, and the

eyepiece, which acts as a simple magnifier with which to view the image formed by the

objective.

Final Image

Rays fromdistant object

FeFo

Final Image


Fo Fe

Final Image atinfinity


FeFo


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A telescope must gather large amounts of light from a dim, distant object; therefore, it

needs a large objective lens to gather as much light as possible and bring it to a bright

focus. Because the objective lens is large, it brings the image of the object to a focus at

some distance away, which is why telescopes are much longer than microscopes. The

eyepiece of the telescope then magnifies that image as it brings it to your eye. The final

image is inverted with respect to object.

The astronomical telescope can be used for terrestrial viewing, but seeing the image

upside down is a definite inconvenience. Viewing celestial objects upside down is no

problem as they are generally spherical. Another inconvenience for terrestrial viewing is

the length of the astronomical telescope, equal to the sum of the focal lengths of the

objective and eyepiece lenses. Terrestrial telescopes use an additional erecting lens.

Normal Adjustment:This is an adjustment where the foci of both the lenses coincide and

final image is produced at infinity.

In normal adjustment M= fo/feTube Length is the distance between objective and eye piece and has a magnitude of

(fo + fe)

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