Refraction of Light by Spherical Lenses (Concave And Convex)

Ankit went to an optician and noticed different types of spectacles there. He observed
that while the glasses of some spectacles were relatively thicker in the middle, other
glasses were thicker on the edge. The glasses of these spectacles are examples of
lenses.

A lens is a transparent material bound by two curved surfaces. Lenses are broadly
classified into two categories depending on their surfaces.

However, we will discuss only double spherical lenses here.

Convex lens

A convex lens is made by joining two spherical surfaces in such a way that it is thicker
at the centre. Its thickness gradually reduces as we move towards the edge.
A convex lens has the ability to converge the light rays to a point that are incident on it.
Thus, it is called a converging lens.

Concave lens

A concave lens is made by joining two curved surfaces in such a way that it is thinner at
the centre. Its thickness gradually increases as we move towards the edge.

A concave lens has the ability to diverge a beam of light rays incident on it. Thus, it is
called a diverging lens.

Differences between a spherical mirror and a lens

The following table lists some common differences between spherical mirrors and
lenses
 Spherical mirror Spherical lens

Image is formed by reflection of light. Image is formed by refraction of light.

A spherical mirror has only one focus. A spherical lens has two foci.

The centre of the spherical mirror is The centre of the spherical lens is termed as
termed as its pole. its optical centre.

The second difference arises due to the fact that a lens has two spherical surfaces (i.e.
it can be made from the arc of two spheres of equal radius).Therefore, light is refracted
twice before it comes out of the lens.

Terms Associated with Lenses:

Optical centre

Optical centre is a point at the centre of the lens. It always lies inside the lens and not
on the surface. It is denoted by ‘O’.

Centre of curvature

It is the centre point of arcs of the two spheres from which the given spherical lens
(concave or convex) is made. Since a lens constitutes two spherical surfaces, it has two
centers of curvature.

The distance of the optical centre from either of the centre of curvatures is termed as
the radius of curvature.
Principal axis

The imaginary straight line joining the two centers of curvature and the optical
centre (O) is called the principal axis of the lens.

Hold a convex lens and direct it against the sunlight. You will find a bright spot appear
on the wall. Can you explain the formation of this bright spot? Light, after refracting
through the lens, converges at a very sharp point. Try to obtain the brightest possible
spot. Now, place a paper on the wall and observe what happens in the next few
minutes.

Focus

The focus (F) is the point on the principal axis of a lens where all incident parallel rays,
after refraction from the lens meet or appear to diverge from. For lenses there are two
foci (F1 and F2) depending on the direction of incident rays.
The distance between the focus (F1 or F2) and the optical centre (O) is known as
the focal length of the lens.

Refraction by Spherical Lenses

Refraction by a spherical lens can be categorized into three cases.

Case I. When the incident light ray is parallel to the principal axis

In this case, the refracted ray will pass through the second focus F 2 for a convex lens,
and appear to diverge from the first focus F1 for a concave lens.

Case II. When the incident light ray emerges from the first focus F1 of a convex
lens, or appears to emerge from the second focus F2 of a concave lens

In this case, light after refraction from both the lenses will move parallel to the principal
axis.
Case III. When the light ray passes through the optical centre (O) of a lens

In this case, the light ray will pass through both the lenses without suffering any
deviation.

Image Formed by Spherical Lenses

Take a convex lens of known focal length. Draw

five equidistant points on a table and put the lens
on the central line. Mark the lines as 2F1, F1, O,
F2, 2F2 (as shown in the figure).

Take a candle and placed it behind 2F1. Observe

the nature and size of the image formed on a screen placed on the other side of the
lens. An inverted image of the candle flame can be seen easily. Now, repeat the
process by changing the position of the candle by bringing it towards the lens, and list
your observations.

Lenses are able to form images by refracting incident light rays. Although, a light source
emits infinite number of light rays in all possible directions, we will consider only two
light rays for the sake of convenience. It allows us to show clearly the nature and
position of the image formed on a screen.
Images Formed by a Convex Lens

A convex lens can produce real as well as virtual images. The nature of the images
formed depends primarily on the position of the object on the principal axis.

Consider the following cases:

The ray diagrams for all the cases are as follows:

I. When the object is at infinity.

II. When the object is beyond the centre of 2F1.

III. When the object is at the centre of curvature 2F1.

IV. When the object is placed between the focus F1 and 2F1.
V. When the object is placed at focus F1.

VI. When the object is placed between the focus F1 and optical centre O.

The position, size, and nature of the image formed by a convex lens can be
summarized in the table below.
 Nature of
Object position Image position Size of image
image

Real and
At infinity At F2 Extremely small
inverted

Real and
Behind 2F1 Between F2 and 2F2 Small
inverted

Same as that of the Real and

At 2F1 At 2F2
object inverted

Between 2F1 and Real and

Beyond 2F2 Enlarged
F1 inverted

Real and
At F1 At infinity Highly enlarged
inverted

Between F1 and O Same side of the lens Enlarged Virtual and erect

Images Formed by a Concave Lens

A concave lens always produces virtual and erect images that are extremely small in
size.

The images formed by a concave lens are divided into two cases.

I. When the object is placed at infinity.

II. When the object is placed beyond 2F1.

The ray diagrams for all the cases are as follows:

I. When the object is placed at infinity.

II. When the object is placed beyond 2F1.

The position, size, and nature of the image formed can be summarized in the table as
follows:

Object position Image position Size of image Nature of

image

At infinity At focus F1 Extremely Virtual and

small exact

Between O and X (X lies beyond Between O and Small Virtual and

2F1) F1 exact

Jai places a sharp edge in front of a spherical lens. He observes that the image formed
is inverted and extremely small in size. Can you guess the nature of the lens used
and the position of the edge? Where should he place this edge to obtain an erect
image?

Lens Formula, Magnification, and Power

Usually in image formation, we are interested in calculating the distance of the image
formed from the lens, size of the image, power of the lens etc. These problems can
be solved with the help of a lens formula. For this, we use a set of sign conventions
applicable for refraction of light by spherical lenses. In this convention, the optical centre
(O) is treated as the origin.

Sigh Convention for Lenses

I. Object is always placed to the left of the lens i.e., the light must fall on the lens from
left to right.

II. All distances parallel to the principal axis are measured from the optical centre of the
lens.

III. Distances along the direction of incident rays (along positive x-axis) are taken as
positive, while distances opposite to the direction of incident rays (along negative x-axis)
are taken as negative.

IV. Distances measured above the principal axis (along positive y-axis) are taken as
positive.

V. Distances measured below the principal axis (along negative y-axis) are taken as
negative.

These sign conventions are represented in the following diagram:

The following table summarizes the sign conventions of concave and convex lenses:

Types of Object Image distance Focal Height of Height of image

lens distance (v) length (f) object (HI)
(u) (Ho)
Real virtual Real Virtual

Convex Negative Positive Negative Positive Positive Negative Positive

Concave Negative * Negative Negative Positive * Positive