RAY OPTICSMODULE 3/3

ATOMIC ENERGY EDUCATION SOCIETY

MUMBAI

REFRACTION THROUGH A PRISM

Consider a ray of light PQ taken as the incident ray passes through a triangular prism ABC.OR is the refracted ray and RS is the

emergent ray.

The angle of incidence and angle of refraction at the first face AB are i and r1 respectively. The angle of incidence and the angle of

refraction or emergence at the second face AC are r2 and e respectively. The angle between the emergent ray RS and the

direction of the incident ray PQ is called the angle of deviation, .

From the triangle QNR, r1 + r2 + QNR = 180º …………. eqn (1)

In the quadrilateral AQNR, AQN & NRA are right angles . Therefore, the sum of

the other angles of the quadrilateral is 180º.

A + QNR = 180º ………….. eqn(2)

Comparing these two equations (1) and (2) we get

r1 + r2 = A ……..eqn(3)

From the MQR, is the exterior ,it can be written as

=MQR+ MRQ= (i – r1 ) + (e – r2 )

= i + e – A …………eqn (4)

This equations shows that the angle of deviation depends on the angle of incidence.

At the minimum deviation Dm, the refracted ray inside the prism becomes

parallel to its base.

At the minimum deviation Dm , we have

= Dm, i = e and r1 = r2.

r1 + r2 = A eqn (3) becomes 2r = A and r=

= i + e – A eqn(4) becomes i =

By Snell’s law, the refractive index of the material of the prism is n21 = =

1

2

n

n

r

i

sin

sin

21

sin( ) / 2

sin2

A Dmn

A=

+

For a small angled prism, i.e., for a thin prism, Dm is also very small, and we get = n21 =

solving this we get, = Dm = (n21–1)A

( )2

2

A Dm

A

+

I- Curve

If we plot the angle of deviation Vs angle of incidence we will get

the following graph as shown in the figure

Is called prism formula

2

A

𝐴 + 𝐷𝑚

2

= 𝐷𝑚

Scattering of light

The direction of sunlight is changed by the atmospheric particles when the sunlight travels through the earth’s atmosphere. This

phenomenon is called scattering of light.

Rayleigh scattering law states that the amount of scattering (I) is inversely proportional to the fourth power of the wavelength.

According to this law light of shorter wavelengths is scattered much more than light of longer wavelengths

Let us take ‘a’ be the size of the particle(scatterer) in the atmosphere. The wavelength of light with a particular colour is taken as .

Rayleigh’s scattering law is applicable for a << , that is, the amount of scattering is proportional to 1/ 4..

Rayleigh’s scattering law is not applicable for a >> , For example large scattering objects like raindrops, large dust or ice particles,

all wavelengths are scattered nearly equally in less amount. Thus, clouds which have droplets of water with a >> are generally

white.

At sunset or sunrise, the sun’s rays have to travel through a larger distance in the

atmosphere. Most of the blue and other shorter wavelengths are removed by

scattering. The least scattered light reaching our eyes and the sun and the sky

appears reddish near the horizon.

𝐼𝛼1

𝜆4

Blue colour of sky: Blue color has a shorter wavelength and scattered more hence the sky appears bluish during noon.

Violet gets scattered even more than blue, having a shorter wavelength but our eyes are more sensitive to blue than violet hence

we see the sky blue.

.

Microscope

when it is at the near point (distance D = 25 cm), it causes some strain on the eye. Therefore, the image formed at infinity is called

normal adjustment (relaxed eye) .

(i) Magnification when the image is formed at D

Linear magnification is ratio of the angle subtended by the image to angle subtended by the object, if placed at D for comfortable

viewing

The linear magnification m can be obtained by using the relation we have

1 11

v vm v

u v f f

= = − = −

Now according to our sign convention, v = - D . Thus,the magnification is

f

Dm +=1

A simple microscope is a double convex lens magnifying glass with a short focal length. When an object is kept near the lens at a

distance f or less than f, and the eye is positioned on the other side close to the lens, an image is produced which is virtual, erect

and bigger than the size of the original object which can be viewed comfortably at a distance 25 cm or more upto infinity.

m = h’ /h where h is the size of the object and h’ the size of the image.

h’

h

vm

u=

1 1 1 1 1 1

f v u u v f= − = −

(1) Simple microscope

(ii) Magnification when the image is at infinity (Normal Adjustment)

The angle subtended by the object whose height is h when it kept at the near point D is given by

0 0tanh

D =

The angle subtended at the eye by the image which is formed at infinity when the object is at f is given by

tan i i

h

f =

The angular magnification is the ratio of the angle (I ) subtended at the eye by the

image when seen through the convex lens to the angle(0) subtended by the object

when it kept at the near point D

0

i

h

Dfm

h f

D

= = =

A simple microscope has a limited maximum magnification ( ≤ 9) for realistic focal lengths

CONCLUSION

When the image is formed at D

f

Dm +=1

𝜃0

From the figure,we can write

𝜃𝑖

From the figure,we can write

Dm

f=

when the image is at infinity D

mf

=

(2) Compound microscope

Compound microscope consists of a lens nearest the object, called the

objective.It will form a real, inverted, magnified image of the object. This

serves as the object for the second lens, the eyepiece.

Eye piece is a simple microscope or magnifier, produces the final image,

which is enlarged and virtual. The first inverted image is formed at the focal

plane of the eyepiece, at a distance appropriate for final image formation at

infinity, or near point D. The final image is inverted with respect to the original

object

Linear magnification by the objective,

'

o

hm

h=

Also Using

' '

0 0

tanhh h L

f L h f

−= = = −

Here h’ is the size of the first image, h is the object size and the focal length of the objective fo. The first image is formed near the

focal point of the eyepiece. The distance between the second focal point of the objective and the first focal point of the eyepiece

(focal length fe ) is called the tube length (L) of the compound microscope

(Note that the distance between the objective and the eye piece is d ,that is d= v0+ue also d=f0+L+fe)

A simple microscope has a limited maximum magnification (≤ 9) for

realistic focal lengths. For much larger magnifications, one uses two

lenses, one compounding the effect of the other. This is known as a

compound microscope

0

(1) o

Leqn m

f = −

'

0 0

0 0

o

v vhm

h u u = = = −

−….Eqn (1)

…..Eqn (2)

L

d

u0

v0ue

When the first inverted image is near the focal point of the eyepiece of

the compound microscope we will get the final image at the near point.

e

ef

Dm +=1

(ii) When the final image is formed at infinity (normal adjustment)

The angular magnification due to the eyepiece is given by

e

ef

Dm =

(i) When the image is formed at near point D

0 e

L Dm

f f= −

(i) when the final image is formed at the near point D

(ii) when the image is formed at infinity (normal adjustment)

0

1e

L Dm

f f

= − +

o em m m=

o em m m=

OR0

0

1e

v Dm

u f

= − +

OR0

0 e

v Dm

u f= −

(using simple microscope result)

(using simple microscope result)

….Eqn (3)

….Eqn (4)

Using Eqn (1),eqn(2) and eqn(3)

Using Eqn (1),eqn(2) and eqn(4)

CONCLUSION

When the image is formed at D

0

1e

L Dm

f f

= − +

0 e

L Dm

f f= −

when the image is at infinity

Linear magnification by the eyepiece,L

d

u0

v0ue

The net magnification of the compound microscope ,

Refracting Telescope The telescope is used to provide angular magnification of distant

objects.

The objective has a large focal length and a much larger

aperture than the eyepiece.

Light from a distant object enters the objective and a real image is

formed in the tube at its second focal point.

The eyepiece magnifies this image producing a final inverted

image.

The magnifying power m is the ratio of the angle β subtended at

the eye by the final image to the angle α which the object subtends

at the lens.

tane

h

u =

−tan

o

h

f =and

e o

e

o

h

u fm

h u

f

−= = = −

From the diagram.

ue

fe

1 1 1

f v u= −

1 1 1 1 1

e e ef D u D u = − = − +

− −

0 0 0

e e

f f fm

u f D

= − = − +

using

(i) Magnification when the final image is formed at D

putting u=-ue,, v = -D and f=fe we get

Astronomical

……..Eqn(1)

Eqn(1) becomes

……..Eqn(2)

1

𝑢𝑒=

1

𝑓𝑒+

1

𝐷

m = −𝑓0𝑓𝑒

1 +𝑓𝑒𝐷

(ii) Magnification When the final image is formed at infinity (normal adjustment)

putting u= - ue, v = and f=fe we get

1 1 1 1 1 10

e e e e ef u u u f = − = + =

−

0 0

e e

f fm

u f = − = −

The length of the telescope tube is fo + fe .

ue

fe

When the final image is formed at D

0 1 e

e

f fm

f D

= − +

When the final image is formed at infinity

0

e

fm

f= −

1 1 1

f v u= − 0

e

fm

f= −

CONCLUSION

The two main considerations with an astronomical telescope are its light gathering power and its resolution or

resolving power.

The light gathering power depends on the area of the objective. With larger diameters, fainter objects can be

observed.

The resolving power, or the ability to observe two objects distinctly, which are in very nearly the same direction,

also depends on the diameter of the objective.

So, astronomical telescopes are always made up of objective of large diameter to get high light gathering power and

resolving power.

The image formed by a telescope is inverted in astronomical telescope.

In terrestrial telescope consists of a pair of inverting lenses to make the final image erect ..

Reflecting telescopes (Cassegrain telescope)

Reflecting telescopes have several advantages.

1) There is no chromatic aberration in a mirror.

2) The parabolic reflecting surface removes the spherical aberration.

3) Mirror can be supported from behind and also has less weight ,therefore mechanical support is much less of a problem.

4) Reflecting telescope can be made large so they have large light gathering power and large diameter of the aperture gives large

resolving power.

Limitations of reflecting telescope is that the objective mirror focusses light inside the telescope tube. One must have an eyepiece

and the observer right there, obstructing some light depending on the size of the observer cage

Since they are normally open ,the mirrors have to be cleaned regularly and need to be replaced after years of service

Reflecting telescope consists of an objective mirror, a secondary mirror and an

eye piece lens

Rays of light coming from a distant object fall on the objective mirror first and

gets reflected by the objective mirror.

The rays reflected by the objective mirror fall on the secondary mirror(convex)

and get reflected

The rays reflected by secondary mirror will be concentrated on a focal point.

The eye piece placed near the focal point magnifies the image and can be seen

finally.

Bibliography

I Acknowledge that

The content and diagrams are taken from NCERT SYLLABUS 2020-21 AND NCERT TEXT BOOK

CLASS XII- PHYSICS

THANK YOU

Dr.A.JEBIN JOEL

PGT(SS)

AECS 4,MUMBAI