Let us now perform an experiment and find out how light gets refracted when it is incident on a rectangular glass slab.
Place a rectangular glass slab on a white sheet of paper fixed on a drawing board.
Trace the boundary ABCD of the glass slab.
Remove the glass slab. Draw an incident ray IO on AB.
Draw the normal at point of incidence (NN1 through O)
Fix two pins P and Q on the incident ray IO.
Place the glass slab within its boundary ABCD.
Looking from the other side of the glass slab fix two pins R and S
such that your eye and the feet of all the pins are in one straight
line.
Remove the glass slab and the pins. Mark the pin points P1, P2, P3 and P4.
Join OO1.It is the refracted ray.
Measure are the angle of incidence, angle of refraction and angle of emergence respectively.
Extend O1E backwards. The emergent ray is parallel to the incident ray.
Refraction through a Glass Slab
The above experiment shows that
When a ray light is passing from air to glass, that is, from a rarer
medium to a denser medium, the refracted ray bends towards the normal
drawn at the point of incidence. In this case
But when the ray of light is passing from glass to air, that is, from a
denser medium to a rarer medium the refracted ray bends away from the
normal. In this case
The emergent ray, O1E which is nothing but the refracted
ray emerging out of the glass slab is parallel to the incident ray. This
means that the refracted ray (emergent ray) has been displaced from its
original path by a distance XY. This displacement is referred to as
lateral displacement.
Lens
is an optical device that is widely used in everyday life. Practically
every adult wears a spectacle which is constructed out of lenses. Lenses are classified according to the geometry and combination of the surfaces.
Lenses are commonly used to form images by refraction in optical instruments such as cameras, telescopes, and microscopes.
Lens Definition
Lens
is an optical device. It is formed by combination of two curved
surfaces, mostly spherical surfaces with a common axis. It allows light
and because of the curvatures and of the material of the lens it also
gets refracted. Lenses are made of glass or transparent polycarbonate or
transparent plastic materials. For the purpose of safety, polycarbonate
materials are preferred for making lenses.
Lenses are
classified as per the types of surfaces used and also the combination of
the surfaces. The shapes of common types of lenses are shown below.
A lens in which both the outer surfaces are
concave outside the plane of lens is called a biconvex lens or simply
convex lens. A lens in which both the outer surfaces are sunk inside the
plane of lens is called a biconcave lens or simply concave lens. Of one
of the surfaces of the lens is plain then it is either called a plano
convex lens or a plano concave lens depending on what the other surface
is.
Lens Focal Length
The relationship between distance of the object (u), distance of the image (v) and focal length (f) of the lens is called lens formula or lens equation.
1f = 1v−1u
This lens formula is applicable to both convex and concave lenses.
We
said that the lens surfaces are spherical. The center of the spherical
surface is called the center of curvature and its distance from the
center of lens is called the radius of curvature. Half the radius of
curvature is defined as the focal length of the lens. The point which is
on the principal axis and away at a focal length from the lens is
called ‘focus’ of the lens. This point is so called because the parallel
rays that enter the lens converge (or deem to converge) together at
this point.
Points
to be remembered while using the lens formula. The values of the known
parameters should be used with their proper sign as per the sign
convention. No sign be assigned to the unknown parameter during
calculations.
Converging Lens
A
biconvex lens or a plano convex lens converges parallel light rays that
enter on one side to a point on the axis on the other side of the lens.
Hence, a biconvex or a plano convex lens is called a converging lens.
The point where the rays actually converge is called the focus of the
lens and the distance of the focus from the lens is called focal length
of the lens.
1. When the Object is Placed between F1 and O:
Formation of Image by a Convex Lens
The image is -
Formed on the same side of the lens
Virtual
Erect
Magnified
2. When the Object is Placed between the Optical Center (O) and first Focus (F1)
Here we consider two rays starting from the top of the object placed at F1 and optical center. The ray parallel to the principal axis after refraction passes through the focus (F2).
The ray passing through the optical center goes through the lens
undeviated. These refracted rays appear to meet only when produced
backwards. Thus, when an object is placed between F1 and O of
a convex lens, a virtual, erect and magnified image of the object is
formed on the same side of the lens as the object.
3. When the Object is Placed at 2F1
The image is -
Formed at 2F2
Real
Inverted
Same size as the object
Here one of the rays starting from the top of the object placed at 2F1
passes through the optic center without any deviation and the other ray
which is parallel to the principal axis after refraction passes through
the focus. These two refracted rays meet at 2F2. Thus, when an object is placed at 2F1 of a convex lens, inverted and real image of the same size as the object is formed at 2F2 on the other side of the lens.
4. When the Object is Placed between F1 and F2
The image is
Formed beyond 2F2
Real
Inverted
Magnified
Let
us consider two rays coming from the object. The ray which is parallel
to the principal axis after refraction passes through the lens and
passes through F2 on the other side of the lens. The ray
passing through the optic center comes out of the lens without any
deviation. The two refracted rays intersect each other at a point beyond
2F2. So, when an object is placed between F1 and 2F1 of a convex lens the image is formed beyond 2F2.
5. When the Object is Placed at F1
The image is -
Formed at infinity
real
Inverted
Magnified
Here
again we consider two rays coming from the top of the object. One of
the rays which is parallel to the principal axis after refraction passes
through F2 and the other ray which passes through the
optical center comes out without any deviation. These two refracted rays
are parallel to each other and parallel rays meet only at infinity.
Thus, when an object is placed at F1 of a convex lens, the image is formed at infinity and it is inverted, real and magnified.
6. When the Object is Placed beyond 2F1
The image is -
Formed between F2 and 2F2
Real
Inverted
Diminished
The ray parallel to the principal axis after refraction passes through F2
and the ray which passes through the optical center comes out without
any deviation. The refracted rays intersect at a point between F2 and 2F2. The image is inverted, real and diminished.
7. When the Object is Placed at Infinity
The image is -
Formed at F2
Inverted
Real
Highly diminished
When the object is at infinity, the rays
coming from it are parallel to each other. Let one of the parallel rays
pass through the focus F1 and the other ray pass through the optical center. The ray which passes through F1
becomes parallel to the principal axis after refraction and the ray
which passes through the optical center does not suffer any deviation.
The
table below gives at a glance the position, size and nature of the
image formed by a convex lens corresponding to the different positions
of the object and also its application.
Position of the object
Position of the image
Nature of the image
Size of the image
Application
Between O and F1
on the same side of the lens
Erect and virtual
Magnified
Magnifying lens (simple microscope), eye piece of many instruments
At 2F1
At 2F2
Inverted and real
Same size
Photocopying camera
Between F and 2F1
Beyond 2F2
Inverted and real
Magnified
Projectors, objectives of microscope
At F1
At infinity
Inverted and real
Magnified
Theatre spot lights
Beyond 2F1
Between F2 and 2F2
Inverted and real
Diminished
Photocopying (reduction camera)
At infinity
At F2
Inverted and real
Diminished
Objective of a telescope
Convex Lens Examples
The simplest example is the magnifying glass. The letters which are too
small to read can easily be read by using a convex lens as a magnifying
glass. The lens is held in such a way that the letters are within the
focal length of the lens. Hence the letters are magnified and in upright
position to make it easy to read. The same principle is used in
spectacles which are used for correction of hyperopia. In olden days,
convex lens were used to ignite by allowing the sun rays to be focused
on the object to be ignited. Here the lens converge the heat rays just
like converging the light rays.
When
a set of parallel rays enter a biconcave lens or a plano concave lens,
it diverges the light rays on the other side of the lens. Hence, a
biconcave or a plano concave lens is called a diverging lens. However
these divergent rays give an impression that they emerge from a point on
the axis at the same side of entry of the rays. It is a virtual point
and not real. This point is called the focus and its distance from the
lens is called focal length of the concave lens.
When the Object is at Infinity:
The image is -
Formed at F1
Erect
Virtual
Diminished
When the Object is Placed between O and F:
The image is -
Formed between O and F1
Erect
Virtual
Diminished
When the Object is Placed at any Position between O and Infinity:
We have learned that the convex lenses converges the parallel rays to
the focus on the other side of the lens. In other words, a ray of light parallel
to the axis of the length will pass through the focus on the other side.
A ray of light which passes through the optical center of the lens proceeds
without any refraction. Hence the intersection of these two rays happens
to be on the other side of the lens, there will be Real Image and
inverted. But if the intersection do not actually occur on the other
side and appears to intersect on the first side, then the image will be Virtual Image and upright.
But in case of concave lenses, the rays always
get diverged and they can only ‘virtually’ intersect on the same side as
the rays enter. Hence the images formed by concave lenses are always
virtual images.
Let us make a table of comparison between these two lenses which can show the differences of their features side by side.
Reflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The law of reflection says that for specular reflection the angle at which the wave is incident on the surface equals the angle at which it is reflected. Mirrors exhibit specular reflection.
Concave Mirror
A concave mirror is a type of curved mirror and
it is concave to the right of the object. The reflective material is
pasted on the side opposite to the object to be placed. The curve of the
mirror is mostly a segment of sphere and hence concave mirrors are also
referred as Concave Spherical Mirror.
When an object is
placed at infinity, the rays coming from it are parallel to each other.
Let us consider two rays, one striking the mirror at its pole and the
other passing through the center of curvature. The ray which is incident
at the pole gets reflected according to the law of reflection and the
second ray which passes through the center of curvature of the mirror
retraces its path. These rays after reflection form an image at the
focus. The image formed is real, inverted and diminished.
The image is
At F
Real
Inverted
Diminished
When the Object is Placed beyond C: The two rays which are considered to obtain the image are:
A ray passing through the center of curvature
A ray parallel to the principal axis. The ray passing through the
center of curvature retraces its path and the ray which is parallel to
the principal axis passes through the focus after reflection. These rays
after reflection meet at a point between C and F. The image is
inverted, real and diminished
The image is
Between C and F
Real
Inverted
Diminished
When the Object is Placed at the Center of Curvature: Here
we consider the two rays, one parallel to the principal axis and the
other passing through the focus. The ray of light which is parallel to
the principal axis passes through the focus after reflection. The other
ray passing through the focus after reflection emerges parallel to the
axis. After reflection these rays meet at the center of curvature to
form an inverted image, which is real and of the same size as the
object.
The image is
At C
Real
Inverted
Same size as object
When the Object is between C and F: Here
we consider a ray of light which is parallel to the principal axis and
another ray passing through the focus. The ray which is parallel to the
principal axis passes through the principal focus and the ray which
passes through the focus after reflection emerges parallel to the
principal axis. The reflected rays meet at a point beyond C and the
image is real, inverted and magnified.
The image is
Beyond C
Real
Inverted
Magnified
When the Object is between C and F:
Here, we consider a ray of light which is parallel to the principal
axis and another ray passing through the center of curvature. The ray
which is parallel to the principal axis passes through the focus and the
ray which passes through the center of curvature retraces its path. The
reflected rays are parallel to each other, and would meet only at
infinity i.e., the image is formed at infinity and it is a real,
inverted, enlarged image of the object.
The image is
At infinity
Real
Inverted
Magnified
When the Object is between the Pole and the Focus : Here
we consider a ray of light which is parallel to the incident ray and
another ray which is passing through the center of curvature. The ray
which is passing through the center of curvature retraces its path and
the other ray which is parallel to the principal axis after reflection
passes through the focus. These rays appear to meet behind the mirror
when the reflected rays are extended backwards. The image is virtual,
erect and magnified.
The nature and size of Concave Mirror Image of an object placed in front of a concave mirror depends on the position of the object with respect to the mirror.
Convex Mirror
A convex mirror
is a curved mirror which has a bulge towards the object. In other
words, the coating of reflex material is done interior of the curved
surface. Mostly the curved surface is a spherical segment. Convex
mirrors are widely used in many practical applications due to its
inherent reflection properties. Convex mirrors used as rear view
mirrors, in staircase on the double-deck buses, vigilance mirrors in big
shops and in showrooms.he intersection of these reflected
rays decide the nature and location of the image.
Let
MM’ be a convex mirror and AB be an object placed at any point in front
of the mirror. The ray AP from point A of the object, parallel to the
principal axis hits the mirror at P and ‘appears’ to pass through the
focus as ray PY’. But in effect it is reflected at P as ray PY. Another
ray AO from the same point is reflected as ray OX but ‘appears’ to pass
through as ray OX’ inside the mirror. The rays PY’ and OX’ intersect
at A’ and forms a virtual image A’B’. When the object AB moves closer to
the mirror, the line YY’ remains the same but the angle POA’ goes
increasing. As a result, the size of the image A’B’ increases. But the
maximum limit of the size of the image is approximately the size of the
object when the object touches the mirror. On the other hand when the
object AB moves away from the mirror, the image becomes smaller and
smaller. Thus, the images in convex mirrors are reduced, upright, and
always lie within the virtual focal length.
The
following rays coming from an object are usually used to construct the
ray diagrams for locating the images formed by a convex mirror.
(i) The
diagram shows a ray of light traveling parallel the principal axis
after reflection from a convex mirror appears to come from its focus
behind the mirror.
(ii)
A ray of light traveling towards the centre of curvature behind the
mirror hits the mirror at 90° and is reflected back its own path. This
is shown in the diagram given below.
are the angle of incidence, angle of refraction and angle of emergence respectively.
But when the ray of light is passing from glass to air, that is, from a
denser medium to a rarer medium the refracted ray bends away from the
normal. In this case 
