Standard/ Class/ Grade – X SSC, CBSE; - VIII ICSELight – Part 1

Gurudatta K Wagh

Contents

Plane mirrorSpherical mirror

ConceptsImages formed by a concave mirror

Ray diagramsSign conventions for reflection by spherical mirrorsMirror formulaMagnification by spherical mirrorLensesConceptsImages formed by a convex lensSign conventionsLens formulaMagnification by a lensPower of lensFunctioning of lens in human beingsProblems of vision and their remediesMyopiaHypermetropiaPresbyopiaApplications

Plane mirror

A mirror is a reflecting surface

It is a plane glass sheet coated on one side with a thin reflecting layer of silver and painted by red colour to protect the coating

Spherical mirror A curved spherical mirror is a part of the spherical reflecting surface

Concepts about spherical mirrors

Centre of curvature (C) The centre of sphere of which the mirror is a part

Pole (P) The centre of the spherical mirror is the pole

Principal axis The straight line passing through the pole and centre of curvature of mirror is its principal axis

Radius of curvature (R) The distance between the centre of curvature and pole of the mirror

Focus of concave mirror (F) The rays parallel to principal axis get reflected from the mirror and meet in front of the mirror at a single point

Focal length (f) The distance between the pole and the focus, f = R/2 or R = 2f

Real image Virtual imageImage formed by converging of rays at a point

Image is formed at a point from where the reflected or refracted light rays appear to diverge

Can be obtained on a screen

Cannot be projected on a screen because the rays do not actually meet there

E.g. image in a camera, image seen on a cinema screen, image produced on human retina

E.g. image made by a plane mirror

Light It is a form of electromagnetic radiation that produces the sensation of vision

Convergence of light Divergence of light When light rays meet at a single point

When light rays from same point source are spread away from each other

To concentrate light at a point convergent beam of light is used

To spread light from a source, diverging beam is used

E.g. Doctors  use  this type of beam to concentrate on teeth, ears and eyes; solar devices

E.g. Street lights, table-lamps

Images formed by a concave mirror

The nature, position and size of image formed depends upon the distance of the object from the surface of the mirror

Images formed by a concave mirror can be studied with the help of ray diagrams

A ray diagram is a specialized pictorial representation used to trace the path of ray of light

For drawing ray diagrams, rules based on laws of reflection are used

Rule 1: If the incident ray is parallel to principal axis, then the reflected ray passes through the focus

Rule 2: If the incident ray is passing through the focus then the reflected ray is parallel to principal axis

Rule 3: If the incident ray passes through the centre of curvature, the reflected ray traces the same path

Position of  object

Position of image

Size of image Nature of image

Figure

At infinity   At focus F Highly diminished

Real and inverted

1

Between infinity and centre of curvature

Between focus F and centre of curvature C

Diminished Real and inverted

2

At the centre of curvature C

At the centre of curvature C

Same size  as that of the object

Real and inverted

3

Between focus and centre of curvature C

Beyond centre of curvature

Magnified Real and inverted

4

At the principal focus F

At infinity Highly magnified

Real and inverted

5

Between the pole and principal focus

Behind the mirror Magnified Virtual and erect

6

Sign conventions for reflection by spherical mirrors

According to the new Cartesian sign convention, the pole (P) of the mirror is taken as origin

The principal axis is taken as  X-axis of the co-ordinate system.  

The sign conventions are as follows:

(1) The object is always placed on the left of the mirror

(2) All distances parallel to the principal axis are measured from the pole of the mirror

(3)  All the distances measure to the right of the origin are taken as positive,  while distance is measured to the left of the origin are taken as negative

(4)  Distances perpendicular to and above the principal axis are taken as positive

(5)  Distances measured to and below the principal axis are taken as negative

(6)  Focal length of convex mirror is positive while that of the concave mirror is negative

Mirror formula

The object distance (u)  is the distance of object from the pole The image distance (v) is the distance of image from the  pole The focal length (f) is the distance of principal focus from the  pole

The relationship between object distance image distance and focal length of a spherical mirror is the mirror formula

The mirror formula is given as:

1/v + 1/u = I/f

This formula is valid in all situations for all spherical mirrors for all positions of the object.

Magnification by spherical mirror

Magnification produced by a spherical mirror is expressed as the ratio of the height of the image (h2)  to the height of the object (h1).  it gives a relative extent to which the image of an object is magnified with respect to the object size.

Magnification =  Height of the  image/  Height of the object

M = h2/ h1 = - v/u

The height of the object is taken to be positive as the object is usually placed above the principal axis

The height of the image is  to be taken as positive for virtual images

However it is to be taken as negative for real images

Lenses

A lens is a transparent material  bound by two surfaces out of which at least one surface  is spherical

Convex lens or double convex lensA  lens having both spherical surfaces, bulging outwardIt  is thicker in the middle than at the edgesThis lens can converge light incident on it

So it is a converging lens

Concave lens or double concave lens

A  lens having both surfaces curved inwards

It is thicker at the edges than at the middle

This  lens can diverge light rays incident on it

So it is a diverging lens

Concepts related to lens

Each lens has two spherical surfaces. Each of these surfaces form a part of a sphere

(1) Centre  of  curvature (C)  It is the centre of the imaginary sphere, which forms the given  lens.  Each lens has two centre of curvatures C1 and C2 respectively

(2) Principal axis It is an imaginary straight line passing through the two centres of curvatures of lens

(3)  Optical centre (O) The central point of lens on the principal axis is its optical centre

When a ray of light passes through the optical centre of a lens it passes without undergoing any deviation

(4) Principal focus of convex lens (F)  When several rays of light parallel to principal axis are incident on a convex lens, they converge at a point on the principal axis. It is the principal focus of the convex lens. Every lens has two principal foci

(5) Focal length (F) The distance between principal focus and optical centre of the lens is the focal length

Images formed by a convex lens

Images formed by a convex lens can be studied with the help of ray diagrams

Ray diagrams are useful to study the position, relative size and nature of the image formed by lenses

Following are the rules for obtaining the images by a convex lens

Rule 1  If the incident ray is parallel to principal axis then the refracted ray passes through focus F

Rule 2  A ray of light passing through the optical centre passes through the optical centre undeviated

Rule 3 If the incident ray is passing through the focus, the refracted ray passes parallel to the principal axis

Incident ray is parallel to principal axis refracted ray passes through focus F

Ray of light passing through the optical centre passes undeviated

Incident ray passes through the focus

Refracted ray passes parallel to the principal axis

Position of the object

Position of the image

Relative size of the image

Nature of the image

Fig. no.

at infinity At focus F2 highly diminished, point sized

Real and inverted

F

beyond 2F1 between F2 and 2F2

diminished real and inverted

E

at 2F1 At 2F2 same size real and inverted

D

between F1 and 2F1

Beyond 2F2

magnified real and inverted

C

At focus F1 at infinity infinitely large and highly magnified

real and inverted

B

between focus F1 and optical centre O

on the same side of the lens as the object

magnified virtual and erect

A

Following diagrams are arranged asA B CD E F

Sign conventions for lens

The focal length of convex lens is positive and that of concave lens is negative

Optical centre of lens is taken as origin and principal axis of lens is taken as X-axis

The sign conventions for lens are similar to the sign conventions of spherical mirror.  Only care should be taken to apply appropriate signs for the values of object distance, image distance, focal length according to the type of lens, height of object and height of image

Lens formula

The relationship between object distance (u), image distance (v), and focal length (f) is lens formula. Here distances should be measured according to sign conventions.The lens formula is given as

1/v - 1/u = 1/f

The lens formula is valid in all situations for any spherical lens

Magnification by a lens

The magnification produced by a lens is the ratio of height of the image and height of the object

Magnification =  height of the image/ height of the object

M= h2/h1

Magnification produced by a lens is also related to the object distance (u)  and image distance (v).

The relationship is given as:

M = v / u

Power of lens (P)

The ability of a lens to converge or diverge a light ray depends on its focal length

E.g.  convex lens of short focal length bends the light rays through large angles,  by focusing them closer to the optical centre  

The degree of convergence of light rays achieved by convex lens is expressed in the terms of power of lens

It is the reciprocal of the focal length

P = 1 / f (in metre)

Unit of power of lens is “dioptre”.

If focal length is expressed in metre the power of lens is expressed in dioptre. Therefore one dioptre is the power of a lens whose focal length is 1 metre.

1 dioptre = 1/ 1 metre

Functioning of lens in human beings

CorneaThe human eye, has a thin membrane, known as cornea.  The light enters the eye through the cornea.  Maximum refraction of light rays entering the eye takes place from cornea.

IrisBehind the cornea, there is a dark muscular diaphragm, called as iris. The colours of iris are different for different people.

Pupil

There is a small opening of variable diameter at the centre of iris called pupil.

The pupil is useful to control and regulate the  amount of light entering the eye.

The pupil contracts if there is too much light while the pupil  dilates in  insufficient light

This tendency of pupil to adjust the opening for light is called adaptation

Structure of human eye

The cornea forms a transparent  bulge on the surface of the eyeball. The eyeball is spherical in shape with a diameter of 2.3 cm.

There is a  transparent  biconvex crystalline body located just behind the pupil. It is a lens. This crystalline lens provides fine adjustment of focal length. With the help of this adjustment, real and inverted image gets formed on the retina.

Retina is the light sensitive screen. It is a delicate membrane. It consists of a large number of light sensitive cells. These cells get activated upon illumination. They generate electric signals. These signals are passed by optic nerves to the brain.

The brain interprets these signals and also processes the information in such a way that we perceive the objects as they are.

The functioning of lens is very important in human eye. The eye adjusts to various object distances by changing the focal length of lens.

For normal eye, in relaxed position of eye muscles, the focal length of eye lens is about 2.5 cm.

The second focal point of eye lens is located at the retina. In this position normal eye can form sharp images of objects located at infinite distance. At this time the lens is thin and distant objects are clearly seen.

Near objectsThe focal length of eye lens decreases while viewing the nearer objects and the lens becomes thick. This gives a sharp image of nearby objects on the retina.

Power of accommodationIt is the ability of the lens of adjusting focal length.The process of focussing the eye at different distances is called accommodation. This is brought about by a change in curvature of the elastic lens making it thinner or fatter.

Distance of distinct vision

It is the minimum distance from the normal eye at which the objects can be seen clearly and distinctly without any strain on the eye. It is about 25 cm

The focal length of the eye lens cannot be decreased below a certain value. We cannot read the words in the book if it is held very close to our eye.

Problems of vision and their remedies

CausesDue to loss of power of accommodation

Weakening of ciliary muscles

Change in the size of eyeball

Irregularities on the surface of cornea

Formation of membrane over the eye lens

Because of refractive defects of eye the vision becomes blurred

Three common refractive defects of vision

Myopia/ near sightednessEye can see nearby objects but unable to see distant objectsThe image of distant object is formed in front of retina

ReasonsCiliary muscles do not relax sufficiently and converging power of eye lens becomes highDistance between eye lens and retina increases as the eyeball is lengthened or lens is curved

CorrectionA suitable concave lens can correct this defectThis lens causes light rays to diverge before they strike the lens of the eyeThe power of the concave lens creates required divergence and forms the image on the retina

LensFocal length of concave lens is negativeThe power of spectacles is negativeThe power of concave lens varies as per the degree of defect

Hypermetropia/ long sightedness

Eye can see distant objects but unable to see nearby objectsThe image of near object falls behind the retina

ReasonsWeak action of ciliary muscles causes low converging power of eye lensThe distance between eye lens and retina decreases due to either shortening of eyeball or flattening of lensFocal length of the eye lens is too long

CorrectionA suitable convex lens can correct this defectThe rays coming from a nearby object are first converged by convex lens and then converged by eye lens to retina

LensFocal length of convex lens is positiveThe power of spectacles is positiveThe power of convex lens varies as per the degree of defect

Presbyopia/ old age hypermetropia

Power of accommodation of eye decreases with ageing. Seeing nearby objects becomes difficult

ReasonCiliary muscles lose the capacity to change the focal length of eye lensSometimes aged people suffer from both myopia and hypermetropia

Correction This requires a bi-focal lensUpper part is concave to correct myopia, useful for distant visionLower part is convex to correct hypermetropia, useful for near vision

Applications

Concave mirrorTorch, headlight Source of light is at focus to obtain a parallel beam of light

Flood lights Source of light is placed beyond the centre of curvature to get intense beam of light

Reflecting mirrors for projector lamps Object is placed at the centre of curvature to obtain an image of the same size

Collecting heat radiations in solar devices Heat radiations from the sun coming from infinity are brought to focus by concave mirror in its focal plane

Shaving mirror, dentist’s mirror Produces an erect, virtual and highly magnified image of an object placed between its pole and focus

Solar furnaces Large concave mirrors concentrate sunlight to produce heat in solar furnace

Convex lensSimple microscope Single convex lens of small focal length for a simple microscope to get 20 times (20X) magnification. Watch repairers, jewellers

Compound microscope Combinations of two convex lenses having short focal lengths used in a compound microscope. Bacteria, viruses, cells, microorganisms

Telescopes Combination of two convex lenses in telescopes

Optical instruments Convex lenses used in instruments like camera, projector, spectrometer

Spectacles Convex lens in spectacles to correct hypermetropia

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