LECTURE ON NUMERICAL LECTURE ON NUMERICAL PROBLEMS IN OPTICSPROBLEMS IN OPTICS

BYBY

KAVITA MONGA(LECTURER-PHYSICS)KAVITA MONGA(LECTURER-PHYSICS)

GOVT POLYTECHNIC COLLEGE GOVT POLYTECHNIC COLLEGE KHUNIMAJRA,KHUNIMAJRA,

MOHALIMOHALI

DATE- 18/4/2013DATE- 18/4/2013

Light :- i) Light is a form of energy which helps us to see objects.

ii) When light falls on objects, it reflects the light and when the

reflected light reaches our eyes then we see the objects.

iii) Light travels in straight line.

iv) The common phenomena of light are formation of shadows,

formation of images by mirrors and lenses, bending of light by a

medium, twinkling of stars, formation of rainbow etc.

• The overall study of how light behaves is called optics. • The branch of optics that focuses on the creation of

images is called geometric optics, because it is based on relationships between angles and lines that describe light rays.

Some Definitions• Absorption

– When light passes through an object the intensity is reduced depending upon the color absorbed. Thus the selective absorption of white light produces colored light.

• Refraction– Direction change of a ray of light passing from one

transparent medium to another with different optical density. A ray from less to more dense medium is bent perpendicular to the surface, with greater deviation for shorter wavelengths

• Diffraction– Light rays bend around edges - new wavefronts are

generated at sharp edges - the smaller the aperture the lower the definition

• Dispersion– Separation of light into its constituent wavelengths when

entering a transparent medium - the change of refractive index with wavelength, such as the spectrum produced by a prism or a rainbow

Absorption

Absorption

Control

No blue/green light red filter

• A lens is an optical device that is used to bend light in a specific way.

• A converging lens bends light so that the light rays come together to a point.

• A diverging lens bends light so it spreads light apart instead of coming together.

• Mirrors reflect light and allow us to see ourselves.• A prism is another optical device that can cause

light to change directions. • A prism is a solid piece of glass with flat polished

surfaces.

• An optical system is a collection of mirrors, lenses, prisms, or other optical elements that performs a useful function with light.

• Characteristics of optical systems are:– The location, type, and magnification of the

image.– The amount of light that is collected.– The accuracy of the image in terms of

sharpness, color, and distortion.– The ability to change the image, like a telephoto

lens on a camera.– The ability to record the image on film or

electronically.

Optical Systems

Reflection• Images appear in mirrors

because of how light is reflected by mirrors.

• The incident ray follows the light falling onto the mirror.

• The reflected ray follows the light bouncing off the mirror.

Reflection

• In specular reflection each incident ray bounces off in a single direction.

• A surface that is not shiny creates diffuse reflection.

• In diffuse reflection, a single ray of light scatters into many directions.

Law of Reflection

The angle of incidence equals the angle of reflection.

The incident ray strikes the mirror.

The reflected ray bounces off.

Law of reflection

• A light ray is incident on a plane mirror with a 30 degree angle of incidence.

• Sketch the incident and reflected rays and determine the angle of reflection.

30o 30o

Mirror

A dentist uses a mirror to look at the back of a second molar (A). Next, she wishes to look at the back of a lateral incisor (B), which is 90° away. By what angle should she rotate her mirror?

A. 90°B. 45°C. 180°

A

B

Specular vs. Diffuse Reflection

Specular Reflection•The surface is flat at distance scales near or above the wavelength of light•It looks “shiny”, like a mirror.

Specular vs. Diffuse Reflection

Diffuse Reflection•The surface is rough at distance scales near or above the wavelength of light•Almost all surfaces reflect in this way!

Two plane mirrors form a right angle. How many images of the ball can you see in the mirrors?

A. 1

B. 2

C. 3

D. 4

Refraction• Light rays may bend as

they cross a boundary from one material to another, like from air to water.

• This bending of light rays is known as refraction.

• The light rays from the straw are refracted (or bent) when they cross from water back into air before reaching your eyes.

RefractionWhen a ray of light crosses from one material to

another, the amount it bends depends on the difference in index of refraction between the two materials.

Refraction

Water

AirRefraction is the bending of light as it passes from one medium into another.

Refraction is the bending of light as it passes from one medium into another.

refraction

N

w

A

Note: the angle of Note: the angle of incidence incidence AA in air in air and the angle of and the angle of refraction refraction AA in in water are each water are each measured with measured with the normal the normal N.N.

The incident and The incident and refracted rays lie in the refracted rays lie in the same plane and are same plane and are reversible.reversible.

The incident and The incident and refracted rays lie in the refracted rays lie in the same plane and are same plane and are reversible.reversible.

Calculate the angle of refraction• A ray of light traveling through air is incident on a

smooth surface of water at an angle of 30° to the normal.

• Calculate the angle of refraction for the ray as it enters the water.

solution• 1) You are asked for the angle of refraction.• 2) You are told the ray goes from air into water at 30 degrees.• 3) Snell’s law: ni sin(θi) = nr sin(θr) ni = 1.00 (air), nr = 1.33 (water)• 4) Apply Snell’s law to find θr. 1.00sin(30°) = 1.33 sin(θr) sin(θr) = 0.5 ÷ 1.33 = 0.376• Use the inverse sine function to find the angle that has

a sine of 0.376.• θr = sin-1(0.376) = 22°

Refraction Distorts Vision

Water

Air

Water

Air

The eye, believing that light travels in The eye, believing that light travels in straight lines, sees objects closer to the straight lines, sees objects closer to the surface due to refraction. Such surface due to refraction. Such distortions are common.distortions are common.

The eye, believing that light travels in The eye, believing that light travels in straight lines, sees objects closer to the straight lines, sees objects closer to the surface due to refraction. Such surface due to refraction. Such distortions are common.distortions are common.

Refraction

But it is really here!!

He sees the fish here….

Depth perception

Apparent Depth

A fish swims below the surface of the water. An observer sees the fish at:

A. a greater depth than it really is.B. its true depth.C. a smaller depth than it really is.

airwater

Virtual Image of Fish

A fish swims directly below the surface of the water. An observer sees the fish at:

A. a greater depth than it really is.B. its true depth.C. a smaller depth than it really is.

airwater

The Index of Refraction

The The index of refractionindex of refraction for a material is the for a material is the ratio of the velocity of light in a vacuum (3 ratio of the velocity of light in a vacuum (3 x 10x 1088 m/s) to the velocity through the m/s) to the velocity through the material.material.

The The index of refractionindex of refraction for a material is the for a material is the ratio of the velocity of light in a vacuum (3 ratio of the velocity of light in a vacuum (3 x 10x 1088 m/s) to the velocity through the m/s) to the velocity through the material.material.

c

vc

nv

Index of refractioncn

v

Examples: Air n= 1; glass n = 1.5; Water n = 1.33

Examples: Air n= 1; glass n = 1.5; Water n = 1.33

Index of Refraction

n

cvmedium

• vmedium is the speed of light in a transparent medium.

• c is the speed of light in a vacuum (c=3.00×108 m/s)

• n is a dimensionless constant: n≥1• n=1 in a vacuum

Index of refractionThe ability of a material to bend rays of light is

described by the index of refraction (n).

Example 1. Light travels from air (n = 1) into glass, where its velocity reduces to only 2 x 108 m/s.

What is the index of refraction for glass?

8

8

3 x 10 m/s

2 x 10 m/s

cn

v vair = c

vG = 2 x 108 m/s

Glass

Air

For glass: n = 1.50

If the medium were If the medium were water: water: nnW W = = 1.331.33. . Then you should show that the velocity Then you should show that the velocity in water would be reduced from in water would be reduced from c c to to 2.26 x 102.26 x 1088 m/s m/s..

Analogy for Refraction

Sand

PavementAir

Glass

Light bends into glass then returns Light bends into glass then returns along original path much as a rolling along original path much as a rolling axle would when encountering a axle would when encountering a strip of mud.strip of mud.

Light bends into glass then returns Light bends into glass then returns along original path much as a rolling along original path much as a rolling axle would when encountering a axle would when encountering a strip of mud.strip of mud.

3 x 108 m/s

3 x 108 m/s

2 x 108 m/s

vs < vp

Snell's law of refraction• Snell’s law is the relationship between the angles

of incidence and refraction and the index of refraction of both materials.

ni sin i= nr sin r Index of

refraction of refractive material

Angle of incidence (degrees)

Angle of refraction (degrees)

Index of refraction of

incident material

Snell’s Law of Refraction

2211 sinsin nn

Snell’s Law

1

2

Medium 1

Medium 2

The ratio of the The ratio of the sine sine of the of the angle of incidence angle of incidence 11 to the to the sinesine of the angle of of the angle of refraction refraction 22 is equal to the is equal to the ratio of the incident ratio of the incident velocity velocity vv11 to the refracted to the refracted velocity velocity vv2 2 ..

The ratio of the The ratio of the sine sine of the of the angle of incidence angle of incidence 11 to the to the sinesine of the angle of of the angle of refraction refraction 22 is equal to the is equal to the ratio of the incident ratio of the incident velocity velocity vv11 to the refracted to the refracted velocity velocity vv2 2 ..

Snell’s Law:

1 1

2 2

sin

sin

v

v

v1

v2

Example 2: A laser beam in a darkened room strikes the surface of water at an angle of 300. The velocity in water is 2.26 x 108 m/s. What is

the angle of refraction?

The incident angle is:The incident angle is:

AA = 90 = 9000 – 30 – 3000 = 60 = 6000

sin

sinA A

W W

v

v

8 0

8

sin (2 x 10 m/s)sin 60sin

3 x 10 m/sW A

WA

v

v

W = 35.30W = 35.30

AirAir

H2

O

303000

W

AA

Snell’s Law and Refractive Index

Another form of Snell’s law can be derived Another form of Snell’s law can be derived from the definition of the index of from the definition of the index of refraction:refraction:

from which c c

n vv n

1 1 21

2 2 12

;

cv v nn

cv v nn

1 1 2

2 2 1

sin

sin

v n

v n

1 1 2

2 2 1

sin

sin

v n

v n

Snell’s law for Snell’s law for velocities and velocities and

indices:indices:

Medium 11

2

Medium 2

A Simplified Form of the Law

1 1 2

2 2 1

sin

sin

v n

v n

1 1 2

2 2 1

sin

sin

v n

v n

Since the indices of refraction for many Since the indices of refraction for many common substances are usually available, common substances are usually available, Snell’s law is often written in the following Snell’s law is often written in the following manner:manner:

1 1 2 2sin sinn n

The product of the index of refraction and The product of the index of refraction and the sine of the angle is the same in the the sine of the angle is the same in the refracted medium as for the incident refracted medium as for the incident medium.medium.

The product of the index of refraction and The product of the index of refraction and the sine of the angle is the same in the the sine of the angle is the same in the refracted medium as for the incident refracted medium as for the incident medium.medium.

Example 3. Light travels through a block of glass, then remerges into air. Find angle of emergence

for given information.

Glass

AiAirr

AiAirr

n=1.5

First find First find GG inside inside glass:glass: sin sinA A G Gn n

505000

G

0sin (1.0)sin 50sin

1.50A A

GG

n

n

G = 30.70

G = 30.70

From geometry, From geometry, note angle note angle GG same same for next interface.for next interface.

G sin sin sinA G G AA An n n Apply to each Apply to each

interface:interface:

e = 500e = 500

Same as entrance Same as entrance angle!angle!

Wavelength and RefractionThe energy of light is determined by the The energy of light is determined by the frequency of the EM waves, which remains frequency of the EM waves, which remains constant as light passes into and out of a constant as light passes into and out of a medium. (Recall medium. (Recall v = fv = f..))

GlassAir

n=1n=1.5A

GfA= fG

GA

; A A A G G Gv f v f

; ;A A A A

G G G G

v f v

v f v

1 1 1

2 2 2

sin

sin

v

v

1 1 1

2 2 2

sin

sin

v

v

The Many Forms of Snell’s Law:

Refraction is affected by the index of Refraction is affected by the index of refraction, the velocity, and the wavelength. refraction, the velocity, and the wavelength.

In general: In general:

Refraction is affected by the index of Refraction is affected by the index of refraction, the velocity, and the wavelength. refraction, the velocity, and the wavelength.

In general: In general:

1 2 1 1

2 1 2 2

sin

sin

n v

n v

1 2 1 1

2 1 2 2

sin

sin

n v

n v

All the ratios are equal. It is helpful to recognize that only the index n differs in the

ratio order.

All the ratios are equal. It is helpful to recognize that only the index n differs in the

ratio order.

Snell’s Law:

Example 4: A helium neon laser emits a beam of wavelength 632 nm in air (nA = 1).

What is the wavelength inside a slab of glass (nG = 1.5)?

nnGG = 1.5; = 1.5; AA = 632 nm = 632 nm

; GA A AG

G A G

n n

n n

(1.0)(632 nm)

1.5421 nmG

Note that the light, if seen Note that the light, if seen insideinside the glass, the glass, would be would be blueblue. Of course it still appears red . Of course it still appears red because it returns to air before striking the because it returns to air before striking the eye.eye.

Glass

AiAirr

AiAirr

n=1.5G

G

Total Internal Reflection

Water

Air

light

The The critical angle critical angle cc is is the limiting angle of the limiting angle of incidence in a denser incidence in a denser medium that results in medium that results in an angle of refraction an angle of refraction equal to 90equal to 9000..

The The critical angle critical angle cc is is the limiting angle of the limiting angle of incidence in a denser incidence in a denser medium that results in medium that results in an angle of refraction an angle of refraction equal to 90equal to 9000..

When light passes at an angle from a When light passes at an angle from a medium of higher index to one of lower medium of higher index to one of lower index, the emerging ray bends away from index, the emerging ray bends away from the normal.the normal.

When the angle When the angle reaches a certain reaches a certain maximum, it will be maximum, it will be reflected internally.reflected internally.

i = r

Critical angle

cc

909000

Total Internal Reflection• Occurs when n2<n1• θc = critical angle.

• When θ1 ≥ θc, no light is transmitted through the boundary; 100% reflection

1

2sinn

nc

Example 5. Find the critical angle of incidence from water to air.

For critical angle, For critical angle, A A = = 909000nnAA = 1.0;= 1.0; n nWW = 1.33 = 1.33

sin sinW C A An n 0sin 90 (1)(1)

sin1.33

AC

w

n

n

Critical angle:

c = 48.80 Water

Air

cc

909000

Critical angle

In general, for media In general, for media where where nn11 > > nn22 we find we find

that:that:

1

2

sin C

n

n 1

2

sin C

n

n

Refraction & Dispersion

Light is “bent” and the resultant colors separate (dispersion).Red is least refracted, violet most refracted.

dispersion

Short wavelengths are “bent” more than long wavelengths

refraction

Dispersion by a Prism

Red OrangeYellowGreenBlueIndigoViolet

Dispersion Dispersion is the separation of white is the separation of white light into its various spectral light into its various spectral components. The colors are refracted at components. The colors are refracted at different angles due to the different different angles due to the different indexes of refraction. indexes of refraction.

Dispersion Dispersion is the separation of white is the separation of white light into its various spectral light into its various spectral components. The colors are refracted at components. The colors are refracted at different angles due to the different different angles due to the different indexes of refraction. indexes of refraction.

Dispersion and prisms

• When white light passes through a glass prism, blue is bent more than red.

• Colors between blue and red are bent proportional to their position in the spectrum.

Dispersion and prisms• The variation in

refractive index with color is called dispersion.

• A rainbow is an example of dispersion in nature.

• Tiny rain droplets act as prisms separating the colors in the white light rays from the sun.

a) Lens formula for spherical lenses :- The lens formula for spherical lenses is the relationship between the object distance (u), image distance (v) and focal length (f).The lens formula is expressed as :- 1 1 1 = v u f

b) Magnification produced by spherical lenses :- Magnification for spherical lens is the ratio of the height of the image to the height of the object. Height of the image hi

Magnification = m = Height of the object ho

The magnification is also related to the object distance and image distance. It can be expressed as :- hi v Magnification m = = ho u

Power of a lens :-

The power of a lens is the reciprocal of its focal length (in metres).

I 1

P = or f =

f (m) P

The SI unit of power is dioptre (D).

1 dioptre is the power of a lens whose focal length is 1 metre.

The power of a convex lens is positive ( + ve ) and the power of a concave lens is negative ( - ve ).

Thin Lens Equation

We can mathematically determine where an image will be formed in relation to the optical centre using the thin lens equation.

The Thin Lens Equation

1 = 1 + 1

f di do

Where: f represents the focal lengthdo represents from the object to the lensdi represents from the image to the lens

FF’ 2F2F’

Focal length

f

do

di

The Thin Lens Equation – Example 1

• A converging lens has a focal length of 17 cm. A candle is located 48 cm from the lens. What type of image will be formed, and where will it be located?

example 1 (cont'd)

G: f =

d0 =

U: di = ?

17 cm

48 cm

example 1

1 = 1 + 1 f di do

1 = 1 - 1 di f d0

E:

Rearrange equation:

example 1…almost there!

S:

1 = 1 - 1 di 17 cm 48 cm

1 = 0.03799cm-1

di

di = 1 / 0.03799cm-1

di = 26.327165 cm = 26 cm

The image of the candle is real and will be about 26 cm from the lens (opposite the object).

S:

S:

example – last step!

Sketch the ray diagram for this problem.

Example 2: Thin Lens Equation and Diverging Lenses

• A diverging Lens has a focal length of 29 cm. A virtual image of a marble is located 13 cm in front of the lens. Where is the marble (the object) located?

• Follow the same steps as before, but be careful with the signs! Refer to your RULES for sign conventions.

Example 2: Ray Diagram Sketch

• Sketch:

Example 2:

G: f = - 29 cmdi = -13 cmd0 = ?

1 = 1 + 1

f do di

1 = 1 - 1d0 f di

1 = 1 - 1d0 -29cm -13cm

1 = 0.042444 cm-1

d0

d0 = 23.560456 cm = 24 cm

The marble is located 24 cm from the lens on the same side as the image.

U:

E:

S:

S:

S:

Magnification Equation

M = hi = - di

ho do

Where:M stands for magnificationhi stands for height of the imageho stands for height of the object

FF’ 2F2F’

h

o

h

i

Magnification Signs and Measurements• Magnification (M) has no units

• M is POSITIVE for an UPRIGHT image• M is NEGATIVE for an INVERTED image

If M is…. Then the image is…• GREATER THAN 1 LARGER than the object• BETWEEN 0 AND 1 SMALLER than the object• EQUAL TO 1 SAME SIZE as the object

Example 3: Finding the Magnification of a CONVERGING lens

• A toy of height 8.4 cm is balanced in front of a converging lens. An inverted, real image of height 23 cm is noticed on the other side of the lens. What is the magnification of the lens?– Follow the same steps as ex 1 & 2 to solve

the problem (just use the magnification equation)

Sketch

Example 3:h0 = 8.4 cm

hi = -23 cm

M = ?

M = hi

ho

M = -23 cm 8.4 cm

M = -2.738095238 = -2.7

The lens has a magnification of -2.7, which means the image is inverted.

G:

U:

E:

S:

S:

S:

Example 4: Magnification of a Diverging Lens

• A coin of height 2.4 cm is placed in front of a diverging lens. An upright, virtual image of height 1.7 cm is noticed on the same side of the lens as the coin. What is the magnification of the lens?

Sketch

Example 4:

h0 = 2.4 cm

hi = 1.7 cm

M = ?

M = hi

ho

M = 1.7 cm 2.4 cm

M = 0.708333 = 0.71

The lens has a magnification of 0.71, which means the image is upright.

G:

U:

E:

S:

S:

S:

Drawing ray diagrams• A ray diagram is the best way to understand what

type of image is formed by a lens, and whether the image is magnified or inverted.

• These three rays follow the rules for how light rays are bent by the lens:

1. A light ray passing through the center of the lens is not deflected at all (A).

2. A light ray parallel to the axis passes through the far focal point (B).

3. A light ray passing through the near focal point emerges parallel to the axis (C).

Reflection of light :- When light falls on a highly polished surface like a mirror most of

the light is sent back into the same medium. This process is called

reflection of light.

Laws of reflection of light :- i) The angle of incidence is equal to the angle of reflection.

ii) The incident ray, the reflected ray and the normal to the mirror at

the point of incidence all lie in the same plane.

Image formed by a plane mirror :- i) The image is erect.

ii) The image is same size as the object.

iii) The image is at the same distance from the mirror as the object is in

front of it.

iv) The image is virtual (cannot be obtained on a screen).

v) The image is laterally inverted.

Spherical mirrors :- Spherical mirror is a curved mirror which is a part of a hollow sphere. Spherical mirrors are of two types. They are concave mirror and convex mirror.

i) Concave mirror :- is a spherical mirror whose reflecting surface is curved inwards. Rays of light parallel to the principal axis after reflection from a concave mirror meet at a point (converge) on the principal axis.

ii) Convex mirror :- is a spherical mirror whose reflecting surface is curved inwards. Rays of light parallel to the principal axis after reflection from a convex mirror get diverged and appear to come from a point behind the mirror.

F

F

Terms used in the study of spherical mirrors :- i) Center of curvature :- is the centre of the sphere of which the mirror is a part (C). ii) Radius of curvature :- is the radius of the sphere of which the mirror is a part (CP).iii) Pole :- is the centre of the spherical mirror (P).iv) Principal axis :- is the straight line passing through the centre of curvature and the pole (X-Y).v) Principal focus :- In a concave mirror, rays of light parallel to the principal axis after reflection meet at a point on the principal axis called principal focus(F). In a convex mirror, rays of light parallel to the principal axis after reflection get diverged and appear to come from a point on the principal axis behind the mirror called principal focus (F).vi) Focal length :- is the distance between the pole and principal focus (f). In a spherical mirror the radius of curvature is twice the focal length. R = 2f or f = R 2

X C F P Y

C – centre of curvature CP – radius of curvature P – pole XY – principal axis F – principal focus PF – focal length

Reflection by spherical mirrors :-i) In a concave mirror a ray of light parallel to the principal axis after reflection passes through the focus.

In a convex mirror a ray of light parallel to the principal axis after reflection appears to diverge from the focus.

C F P P F C

ii) In a concave mirror a ray of light passing through the focus after reflection goes parallel to the principal axis.

In a convex mirror a ray of light directed towards the focus after reflection goes parallel to the principal axis.

C F P P F C

iii) In a concave mirror a ray of light passing through the centre of curvature after reflection is reflected back along the same direction. In a convex mirror a ray of light directed towards the centre of curvature after reflection is reflected back along the same direction.

C F P P F C

iv) In a concave or a convex mirror a ray of light directed obliquely at the pole is reflected obliquely making equal angles with the principal axis.

C F i P i P F C

r r

Images formed by concave mirror :-i) When the object is at infinity the image is formed at the focus, it is highly diminished, real and inverted.

C F P

ii) When the object is beyond C, the image is formed between C and F, it is diminished, real and inverted.

C F P

iii) When the object is at C, the image is formed at C, it is same size as the object, real and inverted.

C F P

iv) When the object is between C and F, the image is formed beyond C, it is enlarged, real and inverted.

C F P

v) When the object is at F, the image is formed at infinity, it is highly enlarged, real and inverted.

C F P

vi) When the object is between F and P, the image is formed behind the mirror, it is enlarged, virtual and erect.

C F P

Images formed by convex mirror :-i) When the object is at infinity, the image is formed at F behind the mirror, it is highly diminished, virtual and erect.

P F

ii) When the object is between infinity and pole, the image is formed behind the mirror, it is diminished, virtual and erect.

P F C

Uses of spherical mirrors :-a) Concave mirrors :- Concave mirrors are used in torches, search lights and head lights of vehicles to get parallel beams of light.

They are used as shaving mirrors to see larger image of the face.

They are used by dentists to see larger images of the teeth.

Large concave mirrors are used to concentrate sunlight to produce heat in solar furnaces.

b) Convex mirrors :- Convex mirrors are used as rear-view mirrors in vehicles. Convex mirrors give erect diminished images of objects. They also have a wider field of view than plane mirrors.

New Cartesian sign convention for spherical mirrors :- i) The object is always placed on the left of the mirror and light from the object falls from the left to the right.

ii) All distances parallel to the principal axis are measured from the pole.

iii) All distances measured to the right of the pole are taken as + ve.

iv) All distances measured to the left of the pole are taken as – ve.

v) The height measured upwards perpendicular to the principal axis is taken as + ve.

vi) The height measured downwards perpendicular to the principal axis is taken as – ve.

Direction of incident light

Distance towards the left ( - ve ) Distance towards the right ( + ve )

Height

downwards ( - ve )

Height

upwards ( + ve )

Concave mirror

Object

Image

Mirror formula for spherical mirrors :- The mirror formula for spherical mirrors is the relationship between the object distance (u), image distance (v) and focal length (f). The mirror formula is expressed as :- 1 1 1 + = v u f

Magnification for spherical mirrors :- Magnification for spherical mirrors is the ratio of the height of the image to the height of the object. Height of the image hi

Magnification = m = Height of the object ho

The magnification is also related to the object distance and image distance. It is expressed as :- hi v Magnification m = = ho u

Refraction of light :- When light travels obliquely from one transparent medium into another it gets bent. This bending of light is called refraction of light.

When light travels from a rarer medium to a denser medium, it bends towards the normal.

When light travels from a denser medium to a rarer medium to a rarer medium, it bends away from the normal.

Denser medium Rarer medium

Rarer medium Denser medium

Normal Normal

Refraction of light through a rectangular glass slab :-

When a ray of light passes through a rectangular glass slab, it gets bent twice at the air- glass interface and at the glass- air interface.

The emergent ray is parallel to the incident ray and is displaced through a distance.

i

e

NormalIncident ray

Emergent ray

Refracted ray

Glass

Air

Normal

r

Glass

Air

Rectangular glass slab

displacement

Angle of emergence

Angle of incidence

Angle of refraction

c) Laws of refraction of light :- i) The incident ray, the refracted ray and the normal to the interface

of two transparent media at the point of incidence, all lie in the same plane.

II) The ratio of the sine of angle of incidence to the sine of angle of refraction is a constant, for the light of a given colour and for the given pair of media.( This law is also known as Snell`s law of refraction.) sine i

= constant sine r

d) Refractive index :- The absolute refractive index of a medium is the ratio of the speed

light in air or vacuum to the speed of light in medium. Speed of light in air or vacuum c

Refractive index = n = Speed of light in the medium v

The relative refractive index of a medium 2 with respect to a

medium 1 is the ratio of the speed of light in medium 1 to the speed of light in medium 2. n21

= Speed of light in medium 1 n 21 = v

1 / v2

Speed of light in medium 2

Spherical lenses :- A spherical lens is a transparent material bounded by two surfaces one or both of which are spherical.

Spherical lenses are of two main types. They are convex and concave lenses.

i) Convex lens :- is thicker in the middle and thinner at the edges. Rays of light parallel to the principal axis after refraction through a convex lens meet at a point (converge) on the principal axis.

ii) Concave lens :- is thinner in the middle and thicker at the edges. Rays of light parallel to the principal axis after refraction get diverged and appear o come from a point on the principal axis on the same side of the lens.

F F

Refraction by spherical lenses :- i) In a convex lens a ray of light parallel to the principal axis after refraction passes through the focus on the other side of the lens. In a concave lens it appears to diverge from the focus on the same side of the lens.

2F1 F1 O F2 2F2 2F1 F1 O F2 2F2

ii) In a convex lens a ray of light passing through the focus after refraction goes parallel to the principal axis. In a concave lens a ray of light directed towards the focus after refraction goes parallel to the principal axis.

2F1 F1 O F2 2F2 2F1 F1 O F2 2F2

iii) In a convex lens and concave lens a ray of light passing through the optical centre goes without any deviation.

2F1 F1 O F2 2F2 2F1 F1 O F2 2F2

Images formed by convex lens :- i) When the object is at infinity the image is formed at the focus F2, it is highly diminished, real and inverted.

2F1 F1 O F2 2F2

ii) When the object is beyond 2F1, the image is formed between F2 and 2F2, it if diminished, real and inverted.

2F1 F1 O F2 2F2

iii) When the object is at 2F1, the image is formed at 2F2, it is the same size as the object, real and inverted.

2F1 F1 O F2 2F2

iv) When the object is between 2F1 and F1, the image is formed beyond 2F2, it is enlarged, real and inverted.

2F1 F1 O F2 2F2

v) When the object is at F1 the image is formed at infinity, it is highly enlarged, real and inverted.

2F1 F1 O F2 2F2

vi) When the object is between F1 and O, the image is formed on the same side of the lens, it is enlarged, virtual and erect.

2F1 F1 O F2 2F2

Images formed by concave lens :- i) When the object is at infinity, the image is formed at the focus F1 on the same side of the lens, it is highly diminished, virtual and erect.

F1 O

ii) When the object is between infinity and F1, the image is formed between F1 and O on the same side of the lens, it is diminished, virtual and erect.

FI O

Sign convention for spherical lenses :- The sign convention for spherical lenses is the same as in spherical mirrors except that the distances are measured from the optical centre (O).

The focal length of a convex lens is positive ( + ve ) and the focal length of a concave lens is negative ( - ve ).

O

Direction of incident light

Distance towards the left (- ve )

Height

downwards ( - ve )

Height

upwards ( + ve )

Convex lens

Object

Image

Distance towards the right ( + ve )