Ray Optics - Vishwa Bharati Public School Optics.pdf · RAY OPTICS BY UMESH TYAGI 1 Ray Optics Ray of Light: The straight line path along which the light travels in a homogeneous

RAY OPTICS BY UMESH TYAGI 1

Ray Optics

Ray of Light: The straight line path along which the light travels in a homogeneous

medium is called a ray of light. The arrow head on the ray gives us the direction of light and number of rays combined together is called beam of light.

Refraction: The phenomenon in which ray of light traveling from one medium to another medium of different optical density, deviates from its original straight line path is called refraction of light.

When light moves from rarer to denser medium it bends towards the normal and when it moves from denser to rarer medium it bends away from the normal.

Refraction of light occurs because the speed of light changes as one moves from one medium to another. Also, the wavelength of light changes, but frequency and phase of the wave remains constant on refraction i.e. no change in phase or frequency occurs.

Laws of Refraction:

First Law [Snell’s Law]-The ratio of the sine of angle of incidence to the sine of angle of refraction is constant for a pair of media in contact.

This constant is equal to the refractive index of second medium w.r.t. first medium. The first medium is one in which incident ray lies and the second medium is one in which the

refractive ray lie. If 1 and 2 denotes the refractive index for the two mediums then

Second law:the incident ray, refracted ray and normal all three lie in the same plane which is plane perpendicular to the refracting surface.

Absolute Refractive Index-Absolute refractive index of the medium is the ratio of

velocity of light in vacuum to the velocity of light in that medium

speed of light in vacuumAbsolute refractive index

speed of light in mediuma m

c

v

1

2

sin

sin

r

i


This implies that the velocity of light decreases if the medium changes times.

Relative Refractive Index-The relative refractive index of second medium w.r.t first

medium is defined as the ratio of the speed of light in first medium to second medium.

2 1

1 2

1 2

speed of light in first medium

speed of light in second medium

v

v

Real and Apparent Depth -

Whenever an object is placed in optically denser medium, like object O placed at the bottom of the container, the ray of light starting from object moves from denser to rarer medium and bends away from normal. Thus a virtual image of the object is formed at I. Then, distance OA is called real depth and IA is called apparent depth of object.

Now, sin and sinAB AB

i rOB IB

Using Snell‟s law,sin 1

sin

ABOB

ABIB

i IB IB

r OB OB

If angles are small then OB OA and IB IA

Here,„t‟ denotes the real depth of the object.

Lateral Shift-It is the perpendicular distance between the incident ray and the

emergent ray.

In ∆BNC, ( ) cosBN BC r

/ cos (1)BC t r

In ∆BCF, ( )sin(i r) (2)CF BC

From equation (1) and (2), we get-

depthApparent

depthReal

IA

OA

Normal Shif,

OA tx OA IA OA t

1 x = t 1 -

μ

i

N’

N

A

B

C

D

E

F d

(i-r)

r

e=i

t


sin(i r)

cos

td

r

Factors- (i) Thickness of medium, (ii) Angle of incidence and (iii) Nature of medium i.e.

refractive index.

Refraction through Compound Plate:

Consider a compound plate made of two materials with refractive index b and c

(c>b). A ray of light incident on ray moving from rarer to denser medium bends towards the normal. Using Snell‟s law,

Similarly, at face M1M1 it suffers refraction and using Snell‟s law,

Finally at surface M2M2 it suffers refraction and comes out parallel to incident ray as all the refracting surfaces are parallel.

Multiply, all three equations,

Total Internal Reflection:

This phenomenon in which a ray of light is reflected back into the same medium when enters from denser to rarer medium and the angle of incidence is greater than the critical angle is called as the total internal reflection.

Consider a source of light S situated in denser medium say water. As the rays move from denser to rarer medium they bends away from the normal. If we go on increasing the angle of incidence angle of refraction also goes on increasing (according to Snell‟s law). At one particular angle of incidence, angle of refraction becomes 90º. The angle of incidence for which the angle of refraction is 90º is called critical angle.

1

1

sin

sin

r

ib

a

cb

r

r

2

1

sin

sin

ac

r

r

1

2

sin

sin

ac

acc

bb

a

ac

cb

ba

1

1


If angle of incidence is increased further the ray gets totally reflected back into the same medium instead of refraction. At critical angle, ic, r = 90.

Applications of Total Internal Reflection:

1.Mirage Formation: It is an optical illusion which takes place in hot countries. The layers of earth in contact with the earth are hooter and rarer whereas the upper layers are colder and denser. When the ray of light moves downwards after reflection from object like tree it moves from denser to rarer medium. The angle of incidence goes on increasing with refraction from each layer of atmosphere. At a particular layer, the angle of incidence becomes greater than critical angle and the ray of light suffers total internal reflection. Thus, a virtual and inverted image of the object is formed on the ground. These virtual images produces the impression of reflection from water due to atmospheric disturbance.

2. Optical Fibers: Optical fibers are the very long and fine threadsmade of quartz or glass. (Diameter of 10—4 cm, with refractive index 1.7). These threads are coated with a thin layer of material of lower refractive index. This coating is called as cladding. Ray of light entering from one side undergoes about 10 - 12thousand reflections per meter and comes out from other end.

Optical fibers can be put to number of application;

(i) They can be used to transmit high intensity laser light insider the body.

c

c

i

i

sin

1

90sin

sin

21

12


(ii) They can be used in the field of communication in sending video and audio signals from one place to another.

(iii) They are used in endoscopy to see images of body‟s internal parts

(3) Totally Reflecting Prism-

An isosceles right angle prism acts as a totally reflecting prism and it works on the

principle of TIR.

This prism can be used to deviate the rays of light by 900 or 1800. It can also be used

to invert the erect image of an object.

Refraction through Spherical Surfaces:

A spherical surface is formed if the refracting surface forms the part of a sphere. The surface is said to be convex if it bulges towards the rarer medium side and it is concave surface if it bulges towards denser medium side.

Sign Conventions:

1. All the distances are measured from pole of spherical surfaces.

2. The distances measured in the direction of incident ray are taken as positive while opposite of it are taken as negative.

Assumptions:

1. The objects are assumed to be point objects lying on the principal axis.

2. The aperture of spherical surface is small.

3. Incident ray, refracted ray and normal makes very small angle with principal axis.

Deviation by 900 Deviation by 1800


(1) WhenRay of light Moving from Rarer to Denser Medium:

a)With convex surface towards rarer (Real Image):

Consider an object O lying on the principal axis. The ray moves from rarer to denser medium and it bends towards the normal and the bending is just sufficient to

make the refracted ray meets the principal axis at I. The refracted ray makes angle β with the principal axis and r with the normal. Using Snell's law,

1 2sin sinri

If angle of incident and refraction are small, then,

sin sini i and r r

1 2r (1)i

In ∆OAC i = + and

In ∆IAC r =

(because exterior angles are equal to interior opposite angles)

Putting the values of I and r in equation (1)

1 ( + ) = 2 ()

2 1 = 1 + 2 …(2)

As angle , and are small,


Substituting these values in (2), we obtain,

(b) With convex surface towards rarer (Virtual Image):

In this case incident ray OA moving from rarer to denser bends towards the normal but the bending is not sufficient to make it move towards principal axis. Thus, a virtual image of object is formed at I. Using Snell's law,

If the angle of incidence and refraction are small then sin i ~ i and sin r ~ r,

Also, i = + and r = +

(because exterior angles are equal to interior opposite angles)

1 ( + ) = 2 ( + )

(21) = 1 2 …(1)

CP

AP

CP

AP

IP

AP

IP

AP

OP

AP

OP

AP

'

'

'tan

'

'

'tan

'

'

'tan

vuR

IP

MP

OP

MP

CP

MP

2112

1

2

1

1

1

12

'

1

2

sin

sin

r

i

rir

i21

1

2

)',','

small, is aperture (as

CPCPAPAPOPOP


Substituting the values of , , in (1), we obtain

(2) With Concave towards Rarer Medium:

The ray of light starting from point object O lying on the principal axis moves towards the normal as it moves from rarer to denser medium and virtual image of the object is formed at I. Using Snell's law

If the angle of incidence and refraction are small then sin i ~ i and sin r ~ r,

where

i = and r =

1 () = 2 ( + )

(21) = 1 + 2 …(1)

Substituting the values of , , in (1), we obtain

uvR

vuR

IP

MP

OP

MP

CP

MP

2112

2112

1

2

1

1

1

12

')(

1

2

sin

sin

r

i

rir

i21

1

2


Similarly, we can prove the identical results for light moving from denser to rarer medium.

Lens:

A portion of refracting material bound between two spherical surfaces out of which at least one surface is curved is called as lens.

Types of Lenses-

(i) Convex or Conversing lens- A lens is said to be converging if the width of the beam decreases after refraction through it. These lenses are thick at middle and thin at edges. Focal length of converging lens is taken as positive.

(ii) Concave or Diverging Lens- A lens is said to diverging if the width of beam increases after refraction through it. These lenses are thin at middle and thick at edges. Focal length of diverging lens is negative.

Definitions

Regarding Lenses:

Optical Centre: It is a point lying on the principal axis of lens within or outside it, such that ray of light passing through it goes un-deviated. If the two surfaces are of same radii of curvature then optical centre lies exactly in the centre of the lens.

Radius of Curvature (R1& R2): Radius of curvature of a surface of lens is defined as the radius of that sphere of which surface forms a part.

Principal Axis: The line joining centre of curvature of two surfaces and passing through optical centre is called principal axis.

uvR

vuR

IP

MP

OP

MP

CP

MP

1212

2112

1

2

1

1

1

12

')(


Principal Focus: Principal focus of the lens is a point at which beam of light coming parallel to the principal axis actually converse (in case of convex lens) or appears to diverse (in case of concave lens) after refraction through lens.

Focal Length: Focal length of a lens is defined as the distance between focus and optical centre. It is denoted by f.

Focal Planes: It is the plane passing through the principal focus and perpendicular to principal axis.

Rules for image formation- There are three rules

(i) Ray moving parallel to principal axis passes through the focus after refraction. (ii) Ray passing through the focus becomes parallel to principal axis after

refraction from lens. (iii) Ray passing through the optical centre goes undeviated (in case of thin

lenses)

Image Formation by Convex Lens-



Image Formation by Concave Lens-

New Cartesian Sign Convention for spherical Lenses:

(i) All distances are measured from optical centre. (ii) The distance measured in

the direction of incident ray are taken as positive while the distance measured in the opposite direction of incident ray are taken as negative

(iii) Heightsmeasured upwards to principal axis are taken as positive while downwards are taken as negative

Lens Formula:

Lens formula is a relation between focal length of lens with the distance of objects and images.

For Convex lens: (For Real Image)-

Let AB be the object placed on the principal axis and beyond focus F. The ray starting from „A‟ passing through optical centre goes undeviated and the ray moving parallel to principal axis passes through focus. The two ray meet at A1, thus A1B1 is the image of the object AB.


As ABC and A1B1C are similar,

Also, CDF and A1B1F are similar,

Also, CD = AB =>

From (1) and (2),

Dividing by uvf,

For Virtual Image: If the object lies between optical centre and the principal focus

then a virtual image of the object is formed. Again as ABC and ABC are similar.

)1...(111 CB

BC

BA

AB

111 FB

CF

BA

CD

)2...(111 FB

CF

BA

AB

uvvfuf

fv

f

v

u

FB

CF

CB

BC

11

fuv

111


Similarly, as CDF and ABF are similar

From (1) and (2) and CD = AB,

Dividing by uvf,

For Concave Lens-

As ABO and A‟B‟O are similar,

' ' '(1)

A B OB

AB OB

Similarly, as ODF and ABF are similar

' ' '

' ' '(2)

A B B F

OD OF

A B B Fas OD AB

AB OF

From equation (1) and (2), we get-

' '

' '

OB B F

OB OF

OB OF OB

OB OF

Using sign convention-

)1...(111 CB

AC

BA

AB

)2...(111 FB

CF

BA

CD

uvvfuf

fv

f

v

u

FB

CF

CA

AC

1'

fuv

111


( )v f v

u f

v f v

u f

vf uf uv

Dividing by uvf on both sides-

1 1 1

f v u

Linear Magnification: The linear magnification produced by a lens is the ratio of

size of the image to the size of the object.

For virtual image,

Thus, for a convex lens, linear magnification is positive when image is virtual and negative if image is real. Similarly, for concave lens the linear magnification is always positive.

Lens Maker’s formula:This formula is used by the manufacturers to design lenses

of required focal length from a glass of given refractive index.1 2

1 1 1( 1)

f R R

Assumptions made in the derivation of lens maker’s formula-

(i) Lens is very thin. (ii) The aperture of the lens is small. (iii) Object is in the form of a point situated at the principal axis. (iv) Incident and refracted rays makes small angles with principal axis

New Cartesian Sign Convention –

)(

))1(('

(AB)object of size

)B'image(A' of size

1

2 imagerealforu

v

h

hm

fromAC

CAm

u

v

h

hm

1

2

u

v

h

hm

1

2


(i) All distances are measured from optical centre. (ii) The distance measured in the direction of incident ray are taken as positive. (iii) The distance measured in the opposite direction of incident ray are taken as

negative

Consider a thin lens with optical centre C, and the point object O placed on the principal axis of this lens.If the second surface AP2B were absent then first surface AP1B will form the real image of object „O‟.at I1. Thus

2 1 2 1

1 1

(1)v u R

But actually the second surface is present there so I1 acts as an imaginary object for the surface AP2Bwhich forms the final image at I. Thus we can write

1 2 1 2

1 2

(2)v v R

Adding equation (1) and (2), we get

2 1 1 2 2 1 1 2

1 1 1 2

1 1

2 1

1 2

1 1

v u v v R R

v u R R

2 1

1 1 2

1 1 1 1

v u R R

If the object is placed at infinity (u=∞), the image will be formed at the focus, i.e. v f .

2 1 2

1 1 2 1 1 2

1 1 1 1 1 1 11

f R R f R R

1 2

1 1 1= μ -1 -

f R R⟹This is lens maker‟s formula and 2

1

is the refractive index of

lens w. r. t. its surrounding‟s medium.


Similarly, the relation can be proved for concave lens also.

Power of a Lens:

Power of lens is the ability of the lens to converge or diverge a beam of light falling

on it. Mathematically, it is defined as the reciprocal of focal length, i.e. 1

Pf

S.I.unit of power is Dioptre (D), if focal length is measured in meters.

1

( )P Dioptre

f in meters

Or 100

( .)P Dioptre

f in cms

Thus “one diopter is the power of a lens of focal length 1 meter”.

A number of lenses can be combined to increase the magnification (compound microscope), make the final image erect (terrestrial telescope). As each lens has its own magnifying power, the resultant magnification is the product of magnification of individual lenses i.e.

m = m1 m2 . . . . . mn

Lenses in Contact: Equivalent Focal Length-Suppose two lenses L1 and L2 of

focal lengths f1 and f2 are placed in contact to each other as shown in figure.

Let O be a point object on the principal axis of the lens system.

In the absence of lens L2, the first lens L1 will form a real image of object „O‟ at I’.

Using lens formula

1

1 1 1(1)

'f v u

But actually the second lens is present there so the image I‟ acts as a virtual object for second lens L2 which forms its real image at I.

C1 C2

L1 L2

O I I’

v

\ u v’


Thus again using lens formula

2

1 1 1(2)

'f v v

Adding the equation (1) and (2), we get,

1 2

1 1 1 1(3)

f f v u

If f is the equivalent focal length of the combination, then

1 1 1(4)

f v u

From equation (3) and (4). We find that 1 2

1 1 1

f f f

∴ Equivalent power, 1 2

P P P

For n thin lenses in contact, we have 1 2 3

1 1 1 1 1............

nf f f f f

∴ Equivalent power, 1 2 3.............

nP P P P P

Note- If the lenses are separated by a distance d then their equivalent focal length is given by-

1 2 1 2

1 2 1 2

1 1 1,

dand Power P P P d P P

f f f f f

Refraction through Prism:

A prism is a wedge shaped body made from refracting medium bound by two plane faces inclined to each other at same angle. The two plane faces are refracting surfaces and angle between them is known as the angle of prism.


Consider ABC as the prism with AB and AC as the two refracting surfaces. The incident ray PE meets the refracting face AB at E making an angle of incidence i with normal NN1. As it is moving from rarer to denser medium it bends towards the normal making an angle r1. Similarly, at second face itmoves from denser to rarer medium making an angle of incidence r2 and angle of refraction e (or angle of emergence). The angle between incident and refracted ray is called angle of deviation.

1 2

1 2

( ) ( )

(i e) (r ) (1)

FOM FMO

i r e r

r

Again in quadrilateral AOPM,

360

90 90 360

180 (2)

AOP OPM PMA MAO

OPM A

OPM A

Also in OPM,

1 2180 (3)r r OPM

From (2) and (3), we get 1 2(4)A r r

Now from equation (1) and (4), we can find out that

(5)i e A

For prism having small refracting angle A the incident ray makes small angle with prism, thus angle of refraction is also small. Applying Snell‟s law, for refraction at face AB and AC,

1sin sin sin sini r and e r


If the angle of incidence and refraction are small, then 1 2

i r and e r

Therefore from equation (5),

1 2( ) ( 1)r r A A

Factors on which angle of deviation depends:

(i) The angle of incidence (ii) The refractive index of the material of prism

(iii) The wavelength of the light used (iv) The angle of prism

Angle of Minimum Deviation: Prism Formula-

The minimum value of angle of deviation when ray of light passes through the prism is called the angle of minimum deviation. In minimum deviation position,

The adjacent graph shows the variation δof with the angle of incidence I for a given

prism and for a given colour of light and the angle δ depends on i only. The graph

shows that as i increases, the angle δ decreases and reaches a minimum value δmand the increases.

The minimum value of the angle of deviation suffered by a ray on passing through a prism is called the angle of minimum deviation and denoted byδm or Dm.

In the position of minimum deviation it is found that

1 2i e and r r

1 2,

2Afrom A r r we get r

,

2

m

m

and from i e A we have i i A

Ai

Using Snell‟s law, sin

sin

i

r

mA + δ

sin2μ =A

Sin2

Dispersion of Light:


The phenomenon of the splitting of a ray of light into its constituent colours on passing through a prism, is called as dispersion of light.

Cause of dispersion.

The refractive index μ of a material

for wavelength λ is given the Cauchy‟s relation

2 4

B CA

Where A, B and C are the constants which depends upon the nature of material.

Also, for small angled prism, the angle of deviation is given by

( 1)A

R R R V R VNow and hence

Thus the red colour is deviated the least and the violet is deviated the most. Other

colours are deviated by angles between red violetand . So different colours of white

light det dispersed on refraction through a prism.

Angular Dispersion:

This difference of deviation produced in violet and red light is called angular dispersion.

,

( 1) ( 1) A

( ) A

V R

V R

V R

Angular dispersion

A

Dispersive Power:

It is the ability of the prism material to cause dispersion and it is defined as the ratio of the angular dispersion to the mean deviation (i.e. deviation of yellow colour). It is

denoted by 𝜔.

,1

V R V RAngular dispersionDispersive Power

Mean deviation


Note- (1) V R

Y

δ + δδ or δ =

2

(2) As v>r , therefore, dispersive power is always positive.

Scattering of Light:

The phenomenon of the change in direction of light due to the atmospheric particles is called as scattering of light.

Intensity of scatted light depends upon the size of particles. If the size of particles is much smaller than the wavelength of light then Rayleigh law holds good and according to this law, “The intensity of scattered light is inversely proportional to the fourth

power of its wavelength." i.e.

4

1I

If the size of particles (like water droplets in clouds) is larger than the wavelength of light then Rayleigh law does not remain valid and all colours are equally scattered.

.Applications of Scattering of light-

Blue color of Sky: Blue colour of the sky. Blue colour of the sky is due to scattering of sunlight by air molecules. According to Rayleigh's law, intensity of scattered light,

41I .So blue light ofshorter wavelength is scattered much more than red light of

longer Wavelength. When we look atthe sky, the scattered light enters our eyes and this light contains blue component in a large proportion. That is why the sky appears blue.

Note-(1) As r = 2b, therefore, scattering of blue colour will be 16 times more than that of red light. Thus the scattered intensity is maximum for shorter wavelengths

(2) Moon has no atmosphere. There is no scattering of sunlight. The sky appears dark.

Reddishness at Sunset and Sunrise. During sunrise or sunset, the sun is near the horizon. Sunlight has to travel a greater distance. So shorter waves of blue region are scattered away by the atmosphere. Red waves of longer wavelength are least scattered and reach the observer. So the sun appears red.

Clouds appear white. Large particles like raindrops, dust and ice particles do notscatter light in accordance with Rayleigh's law, i.e., their scattering power is not selective. Theyscatter light of all colours almost equally. Hence the clouds which have droplets of water witha >>λ are generally white.


Danger signals are red. According to Rayleigh's law, the intensity of scattered light is inversely proportional to the fourth power of Wavelength. In the visible spectrum, red colour has the largest wavelength, it is scattered the least. Even in foggy conditions, such a signal covers large distances without any appreciable loss of intensity due to scattering. Therefore, red coloured signals are preferred.

Rainbows: The rainbow is nature’s most spectacular display of the spectrum of light, produced by refraction, dispersion and internal reflection of sunlight by spherical rain drops. It is observed when the sun shines on rain drops, during or after a shower. An observer standing with his back towards the sun observes in the form of concentric circular arcs (bows) of different colours in the horizon. The inner brighter rainbow is called the primary rainbowand the outer fainter rainbow is called the secondary rainbow.

The primary rainbow is formed by rays which undergo one internal reflection and tworefractions and finally emerge from the raindrops at minimum deviation. The red rays emergefrom the water drops at one angle of 43° and theviolet rays emerge at another angle of 41°. Theparallel beam of sunlight getting dispersed atthese angles produces a cone of rays at theobserver‟s eye, as shown in Fig. Thus therainbow is seen as a colourful arc, with its inneredge violet and outer edge red in colour.

The secondary rainbow is formed by therays which undergo two internal reflections andtwo refractions before emerging from the waterdrops at minimum deviation. Due to two internalreflections, the sequence of colour in secondaryrainbow is opposite to that in the primaryrainbow. Here the inner red rays emerge from thewater drops at angle of 51° and the outer violetrays emerge at angle of 54°.


Optical Instruments

The instruments used to see the tiny or heavenly bodies are known as optical instruments.

Simple Microscope:

A convex lens of short focal length acts as a simple microscope when the object is placed between the optical centre and focus of the lens. In this position of object convex lens forms the magnified image behind the object.

In the figure object AB which when viewed by an unaided eye cannot be seen distinctly. A convex lens is then interposed between the eye and the object so that the distance 'u' of the object from the lens is less than the focal length of the lens. A virtual, erect and magnified image A'B' will be produced. By adjusting the distance of object image is formed at least distance of distinct vision (D=25cm for a healthy eye).

Magnifying Power: It is the ratio of angle subtended by the image at the eye to the

angle subtended by the object at the eye when both are placed at least distance of distinct vision.

Since the virtual image is formed at least distance of distinct vision (D), therefore v = -D, Using Lens Formula,

)1...('

'

'

tan

tan

1 u

D

CB

CB

CB

BA

CB

AB

PowerMagnifying


Multiplying both sides by D, we get,

From (1) and (2),

Compound Microscope:

It is used to see the tiny objects which can‟t be seen by naked eyes.

Construction- It consists of two lenses called as objective and eyepiece. The size and focal length of objective are smaller than that of eyepiece. These lenses are fitted at one end of two hollow metallic tubes open at both ends. These tubes can be inserted into each other with the help of rack and pinion arrangement to change the distance between the two lenses.

Working- Let AB be an object situated on the principal axis at distance greater than focal length of the objective. As refraction takes place through the objective O, a real inverted and magnified image A‟B‟ is formed. This image acts as an object for eyepiece. The position of eye piece so adjusted that A’B’falls within its focal length and so the final image A’’B’’ is formed at least distance of distinct vision. Thus, final image A”B” which is highly magnified but is inverted with respect to the object AB is formed by eyepiece.

fuD

fuv

111

111

)2...(1

1

f

D

u

D

f

D

u

D

f

DM 1


Magnifying Power: The magnifying power is defined as the angle subtended by the

final image at the eye to the angle subtended by object when both are placed at least distance of distinct vision from eye.

2

2

2

2

' '/ 'tan

tan " / "

"' '

'o e

A B C AM

A P C A

C AA BM m m

AB C A

For objective lens, o

o

o

vm

u

Again since the lens eyepiece, acts like a simple microscope, so its magnification me is given by,

1e

e

Dm

f

Thus, magnification of compound microscope should be,

1o

o e

v DM

u f

If final image is formed at infinity, then e

e

Dm

f

∴ o

o e

v DM

u f

Astronomical Refracting Telescope:

Telescopes are used to see very far off heavenly bodies.

Construction- It consists of two lenses called as objective lens and eyepiece. The eye piece has small focal length and small aperture than that of objective lens. These lenses are fitted at one end of two hollow metallic tubes open at both ends. These tubes can be inserted into each other with the help of rack and pinion arrangement to change the distance between the two lenses.

Working- A parallel beam of light coming from distance object forms a real, inverted and diminished image at a distance f0 from C1. The image then acts as an object for eye piece, and final image is formed after refraction through eye piece.


(i) Normal Adjustment: If the final image is formed at infinity after refraction

through the eye piece. The magnifying power of telescope is defined as the

ratio of angle β subtended by the image to the angleα subtended by the object at the eye when both are placed at infinity.

2 1

1 2

tan

tan

' '/ C ' '

' '/ ' C B'

M

A B B C BM

A B C B

1

2

'

'

o

e

C B f focal length of objective lens

C B f focal length of eyepiece

∴ o

e

fM

f

The distance between the two lenses, o eL f f .

(ii) When image is at least distance of distinct vision:

If A’B’ lies within the focal length fe of the eye piece, a final virtual but magnified image A”B” is observed. The position of eye piece is so adjusted that final image is formed at least distance of distinct vision D from the eye.

Consider a source of light S situated in denser medium say water. As the rays move from denser to rarer medium they bends away from the normal.


Magnifying Power:

It is the ratio of angle subtended at the eye by the final image formed at least distance of distinct vision to the angle subtended by the unaided eye by the object at infinity.

2

1

1

2

' '/ C 'tan

tan ' '/ '

'

C B'

o

e

A B BM

A B C B

fC BM

u

Using Lens formula, 1 1 1

f v u

1 1 1

e ef D u

1 1 1

e eu f D

1 11o e

o

e e

f fM f M

f D f D

Length of the tube, o eL f f

Cassegrain reflecting telescope-

It consists of a large concave paraboloidal (primary) mirror having a hole at its centre.

This mirror acts as an objective and it is fitted at one end of a hollow metallic tube.

There is a small convex (secondary) mirror between the focus and pole of the primary


mirror. The eyepiece is placed on the axis of the telescope near the hole of the primary

mirror outside the tube.

Working- The parallel rays from the

distant object are reflected by the

large concave mirror. Before these

rays come to focus at F, they are

reflected by the small convex mirror

and are converged to a point I just

outside the hole. The final image

formed at I is viewed through the

eyepiece. As the first image at F is

inverted with respect to the distant object and the second image I is erect with respect

to the first image F, hence the final image is inverted with respect to the object.

Let f0 be the focal length of the objective and fe that of the eyepiece.

For the final image formed at the least distance of distinct vision,

0 1 e

e

f fM

f D

For the final image formed at infinity,

0 / 2

e e

f RM

f f

Advantages of reflecting type telescope over a refracting type telescope:

(i) No chromatic aberration, because mirror is used.

(ii) Spherical aberration gets removed by using a paraboloidal mirror.

(iii) The image is bright, because there is no loss of light due to reflection and

absorption by objective.

(iv) Higher resolution can be obtained by using a mirror of large aperture.

(v) A mirror provides an easier mechanical support over its entire back surface.

(vi) It is difficult and expensive to make large sized lens free from chromatic

aberration and distortions.

Thus reflecting type telescopes are better than refracting type astronomical telescopes.

* * * * * * * * * * * * * * * * *

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