Lenses Class 10 Notes Maharashtra Board

Std 10 Science Part 1 Chapter 7 Lenses Notes Maharashtra Board

Class 10 Science Part 1 Chapter 7 Lenses Notes Maharashtra Board

Lenses:

Where do we see lenses in daily life?

Reading glasses used by old people
Lens in the front door (peephole)
Small magnifying lens used by watchmakers
Spectacles (glasses)
Telescopes

Spherical Mirror

What is a lens?

A lens is a transparent material (like glass or plastic)
It is shaped with two surfaces that bend light
These surfaces are usually part of a sphere

Types of lenses

a) Convex lens (double convex)
1. Both sides bulge outward (puffed up)
2. Thicker in the middle, thinner at the edges
b) Concave lens (double concave)
1. Both sides curve inward (like a cave)
2. Thinner in the middle, thicker at the edges

How does light behave in a lens?

a) A light ray bends (refracts) twice when passing through a lens:
1. Once when entering the lens
2. Once when leaving the lens
b) This bending changes the direction of the light ray

Types of lenses

Cross-sections of convex and concave lenses

Important parts or elements of a lens:

Centre of Curvature (C)

Imagine the lens surfaces as parts of two big spheres.
The centres of those spheres are called the centres of curvature.
A lens has two centres of curvature: C₁ and C₂.

Radius of Curvature (R)

The radius of each of those spheres is called the radius of curvature.
A lens has two radii of curvature: R₁ and R₂.

Principal Axis

An imaginary straight line passing through both centres of curvature.
It’s like the central line running through the lens.

Optical Centre (O)

A point inside the lens on the principal axis.
Light rays passing through O go straight without bending.

Principal Focus (F)

a. For a convex (converging) lens:
1. Light rays parallel to the principal axis come together (converge) at a point.
2. This point is called the principal focus (F₁ or F₂).
b. For a concave (diverging) lens:
1. Light rays parallel to the principal axis spread out (diverge).
2. But they seem to come from a point on the principal axis — that point is the
principal focus (F₁ or F₂).

Focal Length (f)

The distance between the optical centre (O) and the principal focus (F).
It tells us how strongly the lens bends light.

Ray diagram for refraction :

Why use ray diagrams?

To find where the image forms (position)
To know the size of the image (bigger, smaller, same)
To know the nature of the image (real or virtual, upright or inverted)

Images formed by convex lenses:

Following are the three rules to draw ray diagrams of images obtained by convex lenses.

Rule 1: When the incident ray is parallel to the principal axis, the refracted ray passes through the principal focus.

Rule 2: When the incident ray passes through the principal focus, the refracted ray is
parallel to the principal axis.

Rule 3: When the incident ray passes through the optical centre of the lens, it passes without changing its direction.

Real image formed by a convex lens:

Ray 1 (Parallel Ray):

Ray BC from point B goes parallel to the principal axis.
After passing through the lens, it bends and passes through the principal focus F₂ on
the right.

Ray 2 (Optical Centre Ray):

Ray BO from point B goes through the optical centre O.
It continues straight without bending.

Image Formation:

The two refracted rays meet at point B′ (the image of B).
Since point A is on the principal axis, its image forms directly above B′ at A′.
Therefore, A′B′ is the image of AB.

Final Image Characteristics:

Position: Between F₂ and 2F₂ (on the right side).
Nature: Real and inverted.
Size: Smaller (diminished) compared to the object.

Images formed by convex lenses for different positions of the object:

Images formed by concave lenses:

Rules for Drawing Ray Diagrams (Concave Lens):

If the incident ray is parallel to the principal axis, the refracted ray (after bending) appears to come from the focus when extended backward.
If the incident ray passes through the focus, the refracted ray comes out parallel to the principal axis.

Example (Object Between F₁ and 2F₁)

Object PQ is placed between F₁ and 2F₁ in front of the concave lens.

Ray 1 (Parallel Ray)

Ray PA from point P goes parallel to the principal axis.
After refraction, it bends along AD.
When extended backward, AD appears to come from the focus F₁.

Ray 2 (Optical Centre Ray)

Ray PO from point P passes through the optical centre O.
It continues straight without bending.

Image Formation

The two rays meet (when extended) at point P₁ (image of P).
Point Q (on the axis) forms its image at Q₁, directly below P₁.
So, P₁Q₁ is the image of the object PQ.

Final Image Characteristics (Concave Lens)

Nature: Virtual (cannot be caught on a screen), erect (upright).
Size: Smaller (diminished) than the object.

Sign convention:

According to the Cartesian sign convention, the optical centre (O) is taken to be the origin.
The principle axis is the X-axis of the frame of reference. The sign convention is as follows.

The object is always placed on the left of the lens, All distances parallel to the
principal axis are measured from the optical centre (O).
The distanced measured to the right of O are taken to be positive while those
measured to the left are taken to be negative.
Distances perpendicular to the principal axis and above it are taken to be positive.
Distances perpendicular to the principal axis and below it are taken to be negative.
The focal length of a convex lens is positive while that of a concave lens is negative.

Lens formula:

The formula showing the relation between distance of the object (u), the distance
of the image (v) and the focal length (f) is called the lens formula.

The lens formula is same for any spherical lens and any distance of the object from
the lens. It is however necessary to use the sign convention properly.

Magnification (M):

The magnification due to a lens is also related to the distance of the object (u) and that of
the image (v) from the lens.

Power of a lens:

The capacity of a lens to converge or diverge incident rays is called its power (P).
The power of a lens depends on its focal length.
Power is the inverse of its focal length (f); f is expressed in meters.
The unit of the power of a lens is Dioptre (D).

Combination of lenses:

If two lenses with focal lengths f1 and f2 are kept in contact with each other, the
combination has an effective focal length given by

2. If the powers of the two lenses are P1 and P2 then the effective power of their
combination is P = P1 + P2 .
3. Thus, when two lenses are kept touching each other, the power of the combined
lens is equal to the sum of their individual powers.

Human eye and working of its lens:

Cornea

Thin, transparent outer cover on the eye.
Light enters the eye through the cornea.
Most of the bending (refraction) of light happens at the outer surface of the cornea.

Iris

Dark, fleshy screen behind the cornea.
Its color is different for different people (brown, blue, etc.).
It has a small hole in the center called the pupil.

Pupil

The opening at the center of the iris.
Controls the amount of light entering the eye:
a. Bright light → pupil contracts (gets smaller).
b. Dim light → pupil widens (gets bigger).

Eye Lens (Crystalline Lens)

Located just behind the pupil.
Double convex, transparent, flexible.
Adjusts its focal length slightly to focus images properly.

Retina

The inner screen at the back of the eye.
Made of light-sensitive cells.
Creates electric signals when light falls on it.

Optic Nerve & Brain

Electric signals from the retina go to the brain through the optic nerve.
The brain processes these signals so we see objects as they really are.

Focusing on Far vs. Near Objects

For distant objects → the lens becomes flat → focal length increases.
For nearby objects → the lens becomes more rounded → focal length decreases.

Power of Accommodation

The ability of the eye lens to change its focal length to focus on near or far objects.
This adjustment works only within a certain limit.

Construction of human eye

The change in the shape of the lens while seeing distant and nearby objects

The minimum distance of an object from a normal eye, at which it is clearly visible
without stress on the eye, is called as minimum distance of distinct vision.
The position of the object at this distance is called the near point of the eye, for a
normal human eye, the near point is at 25 cm.
The farthest distance of an object from a human eye, at which it is clearly visible
without stress on the eye is called farthest distance of distinct vision. The position
of the object at this distance is called the far point of the eye.
For a normal human eye, the far point is at infinity.

Do you know?

The eye ball is approximately spherical and has a diameter of about 2.4 cm.
The working of the lens in human eye is extremely important.
The lens can change its focal length to adjust and see objects at different distances.
In a relaxed state, the focal length of healthy eyes is 2 cm.
The other focus of the eye is on the retina.

Defects of Vision and their corrections:

Some people can not see things clearly due to loss of accommodation power of the lenses in their eyes.
Because of defective refraction by the lenses their vision becomes faint and fuzzy.
In general, there are three types of refraction defects.

A) Nearsightedness/ Myopia

In this case, the eye can see nearby objects clearly but the distant objects appear
indistinct.
This means that the far point of the eye is not at infinity but shifts closer to the eye.
In nearsightedness, the image of a distant object forms in front of the retina.
There are two reasons for this defect.
a) The curvature of the cornea and the eye lens increases.The muscles near the
lens can not relax so that the converging power of the lens remains large.
b) The eyeball elongates so that the distance between the lens and the retina
increases.
This defect can be corrected by using spectacles with concave lens of proper focal
length.
This lens diverges the incident rays and these diverged rays can be converged by the
lens in the eye to form the image on the retina.
The focal length of concave lens is negative, so a lens with negative power is
required for correcting nearsightedness.
The power of the lens is different for different eyes depending on the magnitude of
their nearsightedness.

Nearsightedness

B) Farsightedness or hypermetropia

In this defect the human eye can see distant objects clearly but cannot see nearby
objects distinctly.
This means that the near point of the eye is no longer at 25 cm but shifts farther away.
The images of nearby objects get formed behind the retina.
There are two reasons for farsightedness.
a) Curvature of the cornea and the eye lens decreases so that, the converging
power of the lens becomes less.
b) Due to the flattening of the eye ball the distance between the lens and retina
decreases.
This defect can be corrected by using a convex lens with proper focal length.
This lens converges the incident rays before they reach the lens.
The lens then converges them to form the image on the retina.
The focal length of a convex lens is positive thus the spectacles used to correct
farsightedness has positive power.
The power of these lenses is different depending on the extent of farsightedness.

Farsightedness

C) Presbyopia

Generally, the focusing power of the eye lens decreases with age.
The muscles near the lens lose their ability to change the focal length of the lens.
The near point of the lens shifts farther from the eye.
Because of this old people cannot see nearby objects clearly.
Sometimes people suffer from nearsightedness as well as farsightedness.
In such a case bifocal lenses are required to correct the defect.
In such lenses, the upper part is concave lens and corrects nearsightedness while the
lower part is a convex lens which corrects the farsightedness.

Apparent size of an object:

Use of concave lenses:

a. Medical equipments, scanner, CD player – These instuments use laser light. For proper
working of these equipments concave lenses are used.
b. The peep hole in door- This is a small safety device which helps us see a large area outside
the door. This uses one or more concave lenses.
c. Spectacles- Concave lenses are used in spectacles to correct nearsightedness.
d. Torch- Concave lens is used to spread widely the light produced by a small bulb inside a
torch. e. Camera, telescope and microscope- These instruments mainly use convex lenses.
To get good quality images a concave lens is used in front of the eyepiece or inside it.

Use of convex lenses:

A) Simple microscope

A convex lens with small focal length produces a virtual, erect and bigger image of an
object.
Such a lens is called simple microscope or magnifying lens.
One can get a 20 times larger image of an object using such microscopes.
These are used for watch repair, testing precious gems and finding their defects.

B) Compound microscope

Compound microscopes are used to study objects like blood cells, cells of plants and
animals and minute living beings like bacteria.
A compound microscope is made of two convex lenses: objective and eye piece.
The objective has smaller cross-section and smaller focal length.
The eye piece has bigger cross section, its focal length is also larger than that of the
objective.
Higher magnification can be obtained by the combined effect of the two lenses.
The magnification occurs in two stages.
The image formed by the first lens acts as the object for the second lens.
The axes of both lenses are along the same line.
The lenses are fitted inside a metallic tube in such a way that the distance between
can be changed.

C) Telescope

Telescope is used to see distant objects clearly in their magnified form.
The telescopes used to observe astronomical sources like the stars and the planets
are called astronomical telescopes.
Telescopes are of two types. 1. Refracting telescope – This uses lenses 2. Reflecting
telescope – This uses mirrors and also lenses.
In both of these, the image formed by the objective acts as object for the eye piece
which forms the final image.
Objective lens has large diameter and larger focal length because of which maximum
amount of light coming from the distant object can be collected.
On the other hand the size of the eyepiece is smaller and its focal length is also less.
Both the lenses are fitted inside a metallic tube in such a way that the distance
between them can be changed.
The principal axes of both the lenses are along the same straight line.
Generally, using the same objective but different eye pieces, different magnification
can be obtained.

D) Optical instrument

Convex lenses are used in various other optical instruments like camera, projector,
spectrograph etc.

E) Spectacles

Convex lenses are used in spectacles for correcting farsightedness.

Persistence of vision:

We see an object because the eye lens creates its image on the retina.
The image is on the retina as long as the object is in front of us.
The image disappears as soon as the object is taken away.
However, this is not instantaneous and the image remains imprinted on our retina
for 1/16th of a second after the object is removed.
The sensation on retina persists for a while. This is called persistence of vision.

How do we perceive different colours?

The retina in our eyes is made up of many light sensitive cells.
These cells are shaped like a rod and like a cone.
The rod like cells respond to the intensity of light and give information about the
brightness or dimness of the object to the brain.
The conical cells respond to the colour and give information about the colour of the
object to the brain.
Brain processes all the information received and we see the actual image of the
object.
Rod like cells respond to faint light also but conical cells do not.
Thus we perceive colours only in bright light.
The conical cells can respond differently to red, green and blue colours.
When red colour falls on the eyes, the cells responding to red light get excited more
than those responding to other colours and we get the sensation of red colour.
Some people lack conical cells responding to certain colours.
These persons cannot recognize those colours or cannot distinguish between
different colours. These persons are said to be colour blind.
Apart from not being able to distinguish between different colours, their eye sight is
normal.

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