The document provides an overview of the principles of ray optics, particularly focusing on the refraction of light, its laws, and applications. It explains key concepts like refractive index, total internal reflection, critical angle, and the operation of various lenses including convex and concave lenses. Additionally, it addresses practical applications such as optical fibers, mirages, microscopes, and the effects of light refraction in everyday life.

1. Ray optics
Refraction of light

2. Refraction of Light
Refraction is the change in the direction of a
ray passing from one medium to another.
The cause of refraction of light :
● The frequency of the refracted ray remains
constant.
● Due to partial reflection and absorption of
light at the interface, the intensity of the
refracted ray will be less than the incident
ray.
● When the light crosses the boundary
between two different media, deviation of
light occurs, resulting in refraction such
that there is a change in wavelength and
speed of light.

3. Refraction in our day to day life
● Twinkling of stars is due to refraction of light.
● Mirage and looming are optical illusions which are a result of
refraction of light.
● A swimming pool always looks shallower than it really is
because the light coming from the bottom of the pool bends
at the surface due to refraction of light.

4. Laws of Refraction of Light
● The incident ray refracted ray, and the normal to the
interface of two media at the point of incidence all lie on
the same plane.
● The ratio of the sine of the angle of incidence to the sine of
the angle of refraction is a constant. This is also known as
Snell’s law of refraction.

5. Refractive index
Refractive index also called the index of
refraction describes how fast light travels
through the material.
Light travels at different speeds in
different medium it travels faster in air
than in solids like glass
Refractive index means how slow light
is travelling in medium 1 compared to
another
Refractive Index of a medium with
respect to vacuum is called absolute
refractive index

6. Refractive index

7. Absolute Refractive Index

8. What is the index of refraction in a medium where the speed of light is 1.5×108 m/s?
What is the speed of light in water whose refractive index is 1.33?
A ray of light is incident through glass, with refractive index 1.52, on an interface
separating glass and water with refractive index 1.32. What is the angle of refraction if
the angle of incidence of the ray in glass is 30 °?
What should be the angle of incidence of a light ray incident through air on the boundary
separating air from water so that the angle of refraction is 30 °?(refractive index of air is
1 and that of water is 1.32)
A ray of light in air strikes a block of quartz at an angle of incidence of 30˚. The angle of
refraction is 20˚. What is the index of refraction in quartz?(sin 20*=0.342)
A ray of light is traveling through air at an angle of 30∘ to the vertical. It passes into
water and halves its angle to the vertical. What is the index of refraction of water?

9. Optical density
If we compare the refractive indices of two media the
medium which has higher refractive index is known as
optical density medium while the medium which has lower
refractive index is known as optically rarer medium
The ability of a medium to refract light is known as optical
density it depends only on Refractive Index of a given
medium if medium has higher refractive index it has
higher optical density
Refractive index of kerosene oil is 1.44 and that of
water is 1.33.

10. Critical angle & TIR
When light travels from denser medium to rarer
medium, it bends away from the normal. When light
travels from denser medium to rarer medium ,there
is such an angle of incidence for which angle of
refraction becomes 90 degree and refracted ray
goes along the direction of interface of two medium
or along the boundary of separation of two medium.
Such an angle of incidence for which angle of
refraction becomes 90 degree is known as critical
angle.
When light travels from denser medium to rarer
medium, if the angle of incidence is greater than
critical angle then the refracted ray instead of
emerging out again goes into the same medium.
This is known as total internal reflection.(TIR)
Total internal refraction(TIR)
takes place in two conditions :-
1. When light travels from denser
medium to rarer medium.
2. When angle of incidence is
greater than critical angle

11. Applications of total internal reflection
Mirage: It is an optical illusion due to which we see a
layer of water at a short distance in a desert or a road on
a hot day.
when actually there is no water at all. Mirage is produced
by the total internal reflection of light in upward direction
caused by atmospheric refraction.

12. Optical fiber
A cable which is used to transmit the data
through fibers (threads) or plastic (glass) is
known as optical fiber cable.
low optical power is usually fed through optical
fibers for diagnostic purposes, surgical
procedures generally require the transmission of
high power up to 200 W in cw operation

13. Applications of
optical fiber

14. Prism- minimum deviation
OP is the incidence ray, which is making
the angle i1 with normal, and QR is the
angle of emergence, which is represented
by i2.
A is the prism angle and μ is the
refractive index of the prism.
A=Prism angle, δ=Angle of deviation,
i1=Angle of incidence, i2=Angle of
emergent.
In the case of minimum
deviation,∠r1=∠r2=∠r
A=∠r1+∠r2
SO, A=∠r+∠r=∠2r;=>∠r=A/2
A+δ=i1+i2 (∵ In the case of minimum
deviationi1=i2=i and δ=m)
So, A+δm=i+i=2i
Now, i=(A+δm)/2
Now, from snell's rule,μ=sin i/sin r

15. Derivation for prism equation

17. Refraction through glass slab:

18. Lateral displacement is maximum for violet colour light as the wavelength of violet
light is minimum
Lateral displacement is minimum for red colour light as the wavelength of red
colour light is maximum

19. LENSES
A lens is an optically transparent medium bounded by two spherical refracting surfaces
or one plane and one spherical surface.
Lens is basically classified into two types. They are: (i) Convex Lens (ii) Concave Lens
(i) Convex or bi-convex lens: It is a lens bounded by two spherical surfaces such that
it is thicker at the centre than at the edges. A beam of light passing through it, is
converged to a point. So, a convex lens is also called as converging lens.
(ii) Concave or bi-concave Lens: It is a lens bounded by two spherical surfaces such
that it is thinner at the centre than at the edges. A parallel beam of light passing through
it, is diverged or spread out. So, a concave lens is also called as diverging lens.

20. Other types of Lenses
Plano -convex lens: If one of the faces
of a bi-convex lens is plane, it is known as
a plano-convex lens.
Plano-concave lens: If one of the faces
of a bi-concave lens is plane, it is known
as a plano-concave lens.

21. Rules for drawing a ray diagram in case of a lens
Light ray parallel to principal
axis :
The ray of light passing
parallel to the principal axis
will pass through the focus
Light ray through the
focus(F):
The ray of light passing
through the principal
focus after refraction
passes parallel tothe
principal axis

22. Rules for drawing a ray diagram in case of a lens
Light ray through
optic center (O):
The light ray passing
through the optic
center will go
undeviated even after
the refraction
To draw a ray diagram we have to make sure atleast any 2 rules are used

23. REFRACTION THROUGH A CONVEX LENS
Object placed beyond C (>2F)
When an object is placed behind the center of
curvature(beyond C), a real and inverted image is
formed between the center of curvature and the
principal focus. The size of the image is the
Object at infinity:
When an object is placed at infinity, a
real,inverted image is formed at the principal
focus. The size of the image is much smaller than
that of the object(point sized image)

24. REFRACTION THROUGH A CONVEX LENS
Object placed at C
When an object is placed at the center of curvature, a
real and inverted image is formed at the other center
of curvature. The size of the image is the same as that
of the object
Object placed between F and C
When an object is placed in between the center of
curvature and principal focus, a real and inverted
image is formed behind the center of curvature. The
size of the image is bigger than that of the object

25. Refraction Through a Convex Lens
Object placed at the principal focus F
When an object is placed at the focus, a
real image is formed at infinity. The size of
the image is much larger than that of the
object
Object placed between the principal
focus F and optical centre O
When an object is placed in between
principal focus and optical centre, a
virtual image is formed. The size of the
image is larger than that of the object

26. Applications of Convex Lenses
1. Convex lenses are used as camera lenses
2. They are used as magnifying lenses
3.They are used in making microscope, telescope and slide projectors
4.They are used to correct the defect of vision called hypermetropia

27. Refraction through concave lens :
Object at infinity:
When an object is placed at infinity, a virtual
image is formed at the focus. The size of the
image is much smaller than that of the object
Object anywhere on the principal
axis at a finite distance
When an object is placed at a finite distance
from the lens, a virtual image is formed
between optical center and focus of the
concave lens. The size of the image is smaller
than that of the object

28. APPLICATIONS OF CONCAVE LENSES
1.Concave lenses are used as eye lens of ‘Galilean Telescope’
2. They are used in wide angle spy hole in doors.
3. They are are used to correct the defect of vision called ‘myopia’

29. Sign convention of lens

30. Lens formula

32. Linear Magnification for lens :
Linear Magnification is defined as the ratio of
the size of image formed by refraction from
lens to size of the object.
It is represented by ‘m’

33. An object is placed at a distance of 10 cm from a convex lens of focal length 12 cm .Find
the position and nature of the image.
Given, u=-10cm;f=12cm;v=?
we know
1/f = 1/v - 1/u => 1/12=1/v -1/(-10) =>1/12 =1/v+1/10
1/v=(5-6)/60=1/60
=>1/v=-1/60cm
Hence, image formed on the same side of the lens at a distance 60 cm and the image is
virtual and magnified beyond 2F.
A 4 cm tall object is placed perpendicular to the principal axis of a convex lens of focal
length 24 cm. The distance of the object from the lens is 16 cm. Find the position, size
and nature of the image formed, using the lens formula.
f=+24cm,u=−16cm ,As ∣u∣(16cm)<∣f∣(24cm) ,

36. Power of a lens :(strength of the lens ) :
The power of a lens in Ray Optics is its ability to bend light.
The greater the power of a lens, the greater is its ability to refract light that passes
through it. For a convex lens, the converging ability is defined by power and in a concave
lens, the diverging ability.
The power of a lens is defined as the reciprocal of the focal length. Lens power is
measured in dioptres (D). Converging (convex ) lenses have positive focal lengths, so
they also have positive power values. Diverging (concave ) lenses have negative focal
lengths, so they also have negative power values.
What is the power of a convex lens with a focal length of 25 cm?
f = 25 cm = 0.25 m

37. Factor that affects the focal length of a lens
1. The material the lens is made from
2. The curvature of the lens
3. The thickness of the lens
Power of a lens is reciprocal of its focal length. Power of combined lens is
A lens has a power of -3.33 dioptres. Calculate the focal length and state what type of
lens it is.
Two lenses of power -15D and +5D are in contact with each other. The focal length of
the combination is (a) -20 cm (b) -10 cm (c) +20 cm (d) +10 cm

38. Lens in contact :

39. Lens in contact :
One convex lens and one
concave lens placed is
contact with each other. If
the ratio of their power is
(2/3) and focal length of
the combination is 30 cm,
then individual focal
lengths are ___________ .
(A) 15 cm and – 10 cm
(B) – 15 cm and 10 cm
(C) 30 cm and – 20 cm
(D) – 30 cm and – 30 cm

40. Apparent depth :
Real depth is the actual depth from the surface whereas
apparent depth is the depth which is visible to human eye
this is due to refraction of light in different medium where
object seems higher than it's position
If all the angles are very
small :
From the triangle OPN
If Lr~0=>OP~ON
From the triangle INP
If Li~0=>IP=IN

41. Apparent depth with multiple medium
A vessel of depth x is half filled with oil of refractive index U1 & the other half is filled with
water of refractive index U2 the apparent depth of the vessel when viewed from above is
When a glass slab is placed
on a dot on a paper, it
appears displaced by 2 cm,
viewed normally. What is the
thickness of slab if the
refractive is 1.5.

42. Numericals based on the combination of reflection & refraction
A luminous object is placed at a distance of 30 cm from the convex lens of focal length
20 cm. On the other side of the lens, at what distance from the lens a convex mirror of
radius of curvature 10 cm be placed in order to have an inverted image of the object
coincident with it ?

43. 1. A screen is placed at a distance of 100 cm from an object. The image of the object is formed on
the screen by a convex lens for two different locations of the lens separated by 20 cm. Calculate
the focal length of the lens used.
2. A converging lens is kept coaxially in contact with a diverging lens - both the lenses being of
equal focal length. What is the focal length of the combination?
3.A converging lens is used to read the small print in a contract. The lens is held 9.0 cm from the
print and produces a magnification of +2.5 . Focal length of the lens is 3x cm. Find x

45. Simple microscope has a convex lens
of short focal length. It is held near
the eye to get enlarged image of
small objects.
Let an object (AB) is placed at a point
within the principal focus (u < f) of the
convex lens and the observer’s eye is
placed just behind the lens. As per
this position the convex lens
produces an erect, virtual and
enlarged image (A'B'). The image
formed is in the same side of the
object and the distance equal to the
least distance of distinct vision (D)
(For normal human eye D = 25 cm).
Simple Microscope :

46. Magnification of a simple microscope
The linear magnification m, for the image formed at the near point D, by a simple microscope can be
obtained by using the relation:-m=(v/u) = v((1/v)-(1/f))=(1- (v/f))
Using the sign conventions, v= (-) ive and same as D.Therefore, magnification will be m =(1 +(D/f))
Since D is about 25 cm, to have a magnification of six, one needs a convex lens of focal length, f = 5 cm.
Magnification when the image is at infinity.
Suppose the object has a height h. The maximum angle it can subtend, and be clearly visible (without a
lens), is when it is at the near point, i.e., a distance D.
The angle subtended is then given by:-tan θ0 =(h/D)≈ θ0
To find the angle subtended at the eye by the image when the object is at u.
Therefore, (h’/h) = m = (v/u)
Angle subtended by the image will be;-tan θ1= (h’/-v) = (h/-v) x (v/u)= (h/-u) ≈ θ.
○ The angle subtended by the object, when it is at u=-f.
○ θi =(h/f).
○ The angular magnification is m =( θi/ θ0) =(D/f)

47. Compound Microscope :
Compound microscope is also used to see the tiny objects. It has better magnification
power than simple microscope.
Magnification power of microscopes can be increased by decreasing the focal length of
the lens used. Due to constructional limitations, the focal length of the lens cannot be
decreased beyond certain limit. This problem can be solved by using two separate
biconvex lenses.
Construction : A compound microscope consists of two convex lenses. The lens with the
shorter focal length is placed near the object, and is called as ‘objective lens’ or
‘objective piece’. The lens with larger focal length and larger aperture placed near the
observer’s eye is called as ‘eye lens’ or ‘eyepiece’. Both the lenses are fixed in a narrow
tube with adjustable provision.
Working : The object (AB) is placed at a distance slightly greater than the focal length of
objective lens (u > fo). A real, inverted and magnified image (A'B') is formed at the other

48. Compound Microscope :
side of the objective lens. This image behaves as
the object for the eye lens. The position of the eye
lens is adjusted in such a way, that the image
(A'B') falls within the principal focus of the eye
piece. This eyepiece forms a virtual,enlarged and
erect image (A"B") on the same side of the object
Compound microscope has 50 to 200 times more
magnification power than simple microscope

49. Using tanβ = (h/f0) = (h’/L) Magnification (mo) due to objective = (h’/h) =(L/f0)
Where h’ = size of the first image
h= size of the object;fo = focal length of the objective lens;fe= focal length of the eye-
piece
L (tube length) = Distance between focal length of the second objective lens and the
first focal length of the eye-piece.
When the final image is formed at the near point, then the angular magnification will be
:-
me=(1+(D/fe))
When the final image is formed at infinity, the angular magnification due to the eyepiece
is:-me = (D/fe)
Total magnification will be given as:-m=(mome) =(L/f0)(D/fe)

50. Lens maker formula:
Let us consider the thin lens
shown in the image above
with 2 refracting surfaces
having the radii of
curvatures R1 and R2
respectively.Let the
refractive indices of the
surrounding medium and
the lens material be n1 and
n2 respectively.
Let u = object distance, v =
image distance, R1 & R2
are the radii of curvatures of
surface I and surface II.
Consider the I spherical
surface ABC,

51. Lens maker formula:
Lens maker formula is used to construct a lens with the specified focal length. A lens
has two curved surfaces, but these are not exactly the same. If we know the refractive
index and the radius of the curvature of both the surface, then we can determine the
focal length of the lens by using the given lens maker’s formula:1/f=(μ−1)×(1/R1–1/R2)
1.Find out the focal length of the lens whose refractive index is 2.
Also, the radius of curvatures of each surface is 20 cm and -35
cm respectively.
2.Value of the refractive index of lens is 2.5. The curved surfaces
are having the radius of curvatures 10 cm and -12 cm
respectively. Find out the focal length of the lens.