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# Light – Reflection and Refraction

Light
Light is the form of energy which enables us to see objects. No medium required for propagation of light. Speed of light depends upon the density of medium. Speed of light in vacuum or air is 3 $\times$ 108 m/s.

Properties of Light

• Speed of light in vacuum is 3 $\times$ 108 m/s.
• Light travels in straight path.
• Shadow is formed if an opaque object kept in the path of light.

Types of Objects

(FIG 1)

Reflection
Returning of light by opaque objects is termed as reflection.

Types of Reflection

(FIG 2)

Laws of Reflection

• Incident ray, reflected ray and normal rays lie in a same plain.
• The angle of incidence ($\angle$ i) is always equal the angle of reflection ($\angle$ r).
$\therefore$ $\angle$ I = $\angle$ r

FIG 3

Mirror
Any opaque objects which reflects light in regular way is termed as "Mirror".

Types of Mirror

(FIG 4)

Uses of Mirror

Plane Mirror

• As a dressing mirror
• As a decorative materials
• As a reflector in solar cooker
• In kaleidoscope and periscope

Concave Mirror

• As a saving mirror
• As a reflector in torches , head lights of vehicle

Convex Mirror

• As a side mirror or as a rear view mirror

Image

(FIG 5)

When the rays of light reflected from a mirror actually meet as point or appear to meet at a point an image is formed.

Characteristics of Image Formed By Plain Mirror

• Image is virtual and erected.
• Image distance from the mirror equal to the object distance from the mirror.
• Image is same size as the object.

New Cartesian Sign Convention for Spherical Mirror

1. All distance are measured from the pole of mirror.
2. Distances measured in the direction of incident light are taken as positive.
3. Distances measured in the opposite direction of incident light are taken as "Negative".
4. Upward distances from principal axis are taken as positive.
5. Downward distances from principal axis are taken as negatives.

In Short,

 u v f R h1 h2 Concave Mirror - - - - + - Convex Mirror - + + + + +

Note: If object is placed between pole and focal length, before the concave mirror then 'V' and 'h2' are taken as positive.
Where,
u = Object distance
V = Image distance
f = Focal length
h1 = Object height
h2 = Image height

Relation Between Focal length (f) and Radius of curvature (R)
f = $\frac{R}{2}$ or R = 2f

Relation between 'u', 'v', and 'f'
$\frac{1}{f}$ = $\frac{1}{v}$ + $\frac{1}{u}$

Magnification (Linear Magnification
Ratio of image height to the object height or negative ratio of image distance to the object distance is termed as "Magnification". It is denoted by 'm'.
m = $\frac{h_2}{h_1}$
or, m = $\frac{-v}{u}$
$\therefore$ m = $\frac{h_2}{h_1}$ = $\frac{-v}{u}$

Image Formation by a Concave Mirror

 Position of Object Position of Image Nature of Image Size of Image Infinity At focus (F) Real and inverted Highly diminished Beyond 'C' Between 'F' and 'C' Real and inverted Diminished Centre of Curvature (C) Centre of Curvature (C) Real and inverted Same size as object Between 'C' and 'F' Beyond 'C' Real and inverted Magnified At the Focus (F) At infinity Real and inverted Highly magnified Between pole and focus Behind the concave mirror Virtual and erect Magnified

Ray diagram of image formation by concave mirror

FIG 6

• Object at infinity
• Image formed at 'F'
• Real and inverted
• Highly diminished

FIG 7

• Object is at beyond 'C'
• Image is formed between 'F' and 'C'
• Image is real and inverted
• Diminished

FIG 8

• Object at center of curvature (C)
• Image is formed at center of curvature
• Image is real and inverted
• Image is same size as object

FIG 9

• Object is in between 'C' and 'F'
• Image is formed beyond 'C'
• Image is real and inverted
• Image is magnified

FIG 10

• Object is at focus 'F'
• Image is formed at infinity
• Real and inverted
• Highly magnified

FIG 11

• Object is in between pole (P) and focus (F)
• Image is formed behind the concave mirror
• Image is virtual and erected
• Image is magnified

Image Formation by a Convex Mirror

 S.N Object Position Image Position Nature of Image Size of Image 1. Infinity At focus (F) Virtual and Erected Highly diminished 2. Anywhere between pole and infinity Between 'P' and 'F' Virtual and erected Diminished

Ray diagram of image formation by Convex mirror

FIG 12

• Object at infinity
• Image formed is at focus (F)
• Image is virtual and erected
• Image is highly diminished

FIG 13

• Object can be anywhere between 'pole' and 'infinity'
• Image formed is between 'P' and 'F'
• Image is virtual and erected
• Image is diminished

Refraction of Light
The phenomenon of bending of light when it passes from one medium to another is termed as refraction of light.

• When light ray goes from rarer medium to denser it bends towards normal.
• When light ray goes from denser medium to rarer medium, it bends away from normal.

FIG 14

Causes of Refraction
Change in speed of light when light goes from one medium to another.

Medium
Anything through which light can pass is termed as 'medium'.

Types of Medium

• Optically Denser Medium
The medium through which light travels slow is termed as denser medium.
• Optically Rarer Medium
The medium through which light travels fast is termed as rarer medium.

NOTE: "Optical density of a medium is inversely proportional to the speed of light".

Laws of Refraction

• The incident ray, refracted ray and normal to the surface lie in the same place.
• The ratio of the 'sin' of the incident angle ($\angle$ i) to the 'sin' of the refracted angle ($\angle$ r) is constant for a pair of two media.
e., $\frac{sin \; i}{sin \; r}$ = constant.
This constant is called refraction index of second medium. This law is also known as "Snell's law".

NOTE: "Refractive index of a substance is measured by "Refractometer".

Refractive Index
It is a measure of change in the speed of light when it enters the medium from air.

(FIG 15)

Factors Affecting Refractive Index

• Nature of Medium
• Density of Medium
• Wave length of color of light

NOTE: Lowest refractive index = 1.00 (vacuum)
Highest refraction index = 2.42 (diamond)

Lens
Transparent medium bounded by two refracting surfaces in which at least one surface must be curved is termed as "Lens".

(FIG 16)

FIGURES (6) – 17, 18, 19, 20, 21 & 22

New Cartesian Sign Convention for Lenses

• All the distances are measured from optical center of lens.
• Distances measured in the direction of incident ray taken as positive.
• Distances measured opposite to the direction of incident ray the taken as negative.
• Height above the principal axis is taken as positive.
• Height below the principal axis is taken as negative.

In Brief,

 u v f h1 h2 Convex Lens - + + + - Concave lens - - - + +

NOTE: If object is placed between optical center (O) and focus (F) before convex lens then (V) is taken as negative (-).

Image Formation by Convex lens

 S.N Object Position Image Position Size of Image Nature of Image 1. At Infinity At focus Very small Real and Inverted 2. Beyond 2F1 Between F2 and 2F2 Small Real and Inverted 3. At 2F1 At 2F2 Same Size as the Object Real and Inverted 4. Between F1 and 2F1 Beyond 2F2 Magnetized Real and Inverted 5. At F1 At Infinity Highly Magnified Real and Inverted 6. Between F1 and optical center On the same side where object Magnified Virtual and Erected

Ray diagrams for the formation of image by convex lens

FIG 23

• Object at infinity
• Image is formed at F2
• Real and Inverted
• Very small

FIG 24

• Object beyond 2F1
• Image formed is between
• Real and Inverted
• Small in size

FIG 25

• Object at 2F1
• Image is formed at 2F2
• Real and Inverted
• Same size as object

FIG 26

• Object is in between
• F1 and 2F1
• Image from beyond 2F2
• Real and Inverted

FIG  27

• Object is at F1
• Image is formed at infinity
• Image is highly magnified
• Real and Inverted

FIG 28

• Object is between F1 and optical center of the Lens
• On the same side of the object
• Image is magnified
• Virtual and Erected

Image Formation by Concave Lens

 S.N Object Position Image Position Size of image Nature of Image 1. At Infinity At Focus (F1) Very small Virtual and Erected 2. Anywhere between optical central and infinity. Between the focus F1 and optical center of the lens. Small Virtual and Erected

Ray diagram for the formation of image by concave lens

FIG 29

• Object at infinity
• Image is formed at F1
• Image is very small
• Virtual and Erected

FIG 30

• Object is in between optical center and infinity
• Image is formed between F1 and optical center
• Image is small
• Virtual and erected

Lens Formula
$\frac{1}{f}$ = $\frac{1}{v}$ - $\frac{1}{u}$
where,
f = focal length
v = Image distance
u = Object distance

Magnification Produced by lens
m = $\frac{v}{u}$
m = $\frac{h_2}{h_1}$
$\therefore$ m = $\frac{h_2}{h_1}$ = $\frac{v}{u}$
where,
m = magnification
h1 = object height
h2 = image height
v = image distance
u = object distance

Power of a Lens
The reciprocal of focal length of a lens is called power of lens.  It is denoted by 'P'. S.I unit of power is m-1 (per meter) or diopter (D).
P = $\frac{1}{f_{(in \; meter)}}$

Focal length of combination of two lenses in contact
$\frac{1}{F}$ = $\frac{1}{f_1}$ + $\frac{1}{f_2}$

Power of combination of lens
P = P1 + P2 + . . . .