Light



Light is a form of energy which controls the sense of vision.
Reflection of Light from Curved Mirrors
Difference between Concave and Convex Mirrors
Distinguish between concave and convex mirrors
Concave  mirror  is  a  spherical  mirror  whose  reflecting  surface  is  curved  inwards.  A  Good
example is the driving mirror of a car.
Convex  mirror  is  a  spherical  mirror  whose  reflective  surface  is  curved  outwards.  A  good
example of a convex mirror is a shaving mirror.
General demonstrations of convex and concave mirrors (curved mirrors:
The Terms Principle, Axis, Pole, Principle Focus and Radius of Curvature as
Applied to Curved Mirrors
Explain  the  terms  principle,  axis,  pole,  principle  focus  and  radius of curvature  as applied  to
curved mirrors
Terms used in studying curved mirrors
23



Centre of curvature (C):
the centre of the sphere of which a mirror is a part of.
Radius of curvature (R)
: the radius of sphere of which a mirror is a part of.
Pole ( P)
: the central point of the reflecting surface of spherical mirror ( curved or convex
mirror).
Principal axis:
the straight line joining the centre of curvature (C) and the pole (P).
Principal focus (F):
the point o the principal axis where light rays tend to intersect. This
point is between centre of curvature and the pole.
Principal axis:
the straight line joining the centre of curvature (C) and the pole (P).
Principal focus (F):
the point on the principal axis wher e light rays tend to intersect. This
point is between centre of curvature and the pole.
The Images Formed by a Curved Mirror
Locate the images formed by a curved mirror
Case (1)
When  a  beam  of  light  parallel  and  very  close  to  the  principal  axis,  CL,  is  reflected  from  a
concave mirror, it converges to a point, F, on the principal axis called the principal focus.
24



Case 2
When a ray passes through the principal focus, F, it is reflected parallel to the principal axis.
Case 3
When  a  ray  passes  through  the  centr e  of  curvature,  C,  which  therefore  strikes  the  mirror  at
normal incidence, it is reflected back along its original path.
25



Note
: Concave mirrors have a real focus because light passes through the focus.
The formation of images by concave mirror tends to change as the position of object changes.
Case 1: Image ( I) formed by a concave mirror when the object is beyond C.
Properties of images formed:
1.
The image is between C and F
2.
The image is smaller than the object
3.
The image is inverted (upside down)
4.
The image is real
Case 2: The object is placed at C
26



Properties of image
1.
The image is formed at C
2.
The image has the same size as object
3.
The image is inverted (upside down)
4.
The image is real.
Case 3: The object is placed between C and F
Properties of image formed
1.
The image is real
2.
The image is large than object
3.
The image is formed beyond C
4.
The image is inverted (upside down)
5.
The image is real
6.
The image is large than object
7.
The image is formed beyond
27



8.
The image is inverted (upside down)
Case 4:The object is placed at F
Properties of image:
1.
The image is formed at infinity (x)
2.
The image is formed beyond C
3.
The image is large than object
4.
The image is Real
Case 5:The object is placed between F and P.
Properties of image formed:
1.
The image is virtual
2.
The images is upright
3.
The image is formed behind the mirror
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4.
The image is large than the object
Formation of images in a convex mirror:
Obviously,there isonly one kind of image formed when an object is placed at any position.
Properties of image formed by convex mirror:
1.
the image is virtual
2.
the image is upright
3.
The image is smaller than object (diminished)
4.
The image is formed behind the mirror.
Example 1
An object 2cm long is erected 8cm infront of a concave mirror of radius of curvatur e 10cm. By
using a scale drawing, determine the position, size and nature of image formed.
Data given
Height of object, Ho = 2cm
Object distance, U= 8cm
Radius of curvature, r = 10cm
Focal length,f =8cm
Choose suitable scale.
Say 1cm represents 5cm
From this scale then
Height of object, Ho = 2cm
Object distance, U= 2cm
Focal length, F = 2.5cm
29



Thus,
Image distance, V = X
Image Height, H
=Y
1
The Focal Length of a Concave Mirror
Determine practically the focal length of a concave mirror
Focal length ( f) is the distance between the principal focus and the pole.
Convex and Concave Mirrors in Daily Life
Use Convex and concave mirrors in daily life
Curved mirrors are used as:
1.
Driving mirrors
2.
Shaving mirrors
3.
Reflectors
Question Time 1
Why is convex mirror used as driving mirror?
The convex mirror is used as driving mirror because it provides the wider field of view.
Question Time 2
30



Why concave mirror used as shaving mirror?
Concave mirrors are used as shaving mirrors because they form an enlarged image when held close up.
Refraction of Light
The Concept of Refraction of Light
Explain the concept of refraction of light
Refraction  of  light  refers  tothe  bending  of  light  as  it  passes  through  two  different  medium
because the speed of light tends to change when travelling from one medium to another.
Figure showing refraction of light as it passes from air to glass.
The Angle of Incidence and Angle of Refraction
Measure the angle of incidence and angle of refraction
The angle of incidence  (i)
is the angle between  the  incident  ray of light  and the normal at the
point of incidence.
The angle of Refraction (r)
is the angle between the refracted ray and the normal at the point of
incidence.
The Laws of Refraction
State the laws of refraction
First law of refraction
The First Law of refraction states that "the incident ray, the refracted ray and the normal at the
point of incident are located in the same plane.”
31



Second law of refraction
Second  Law of  ref raction  states  that  “when  a  light ray passes  from  one  medium  into another
medium,  the angle of  incidence (i) and corresponding angle  of refraction( r)  are  such that  the
ratio of sine of the angle of incidence to the sine of the angle of refraction (sini/sinr) is a constant
value called the ref ractive index."
Note
: The Second Law of Refraction is called Snell's Law in honour of a Dutch scientist named
Snell (1591 – 1626) who first described it.
The Refraction Index of a Material
Determine the refraction index of a material
Refractive index (n) is the ratio of the sine of the angle of incidence to the sine of the angle of
refraction.
n = Sini/Sinr OR
Refractive index (n) is the ratio of the velocity of light in air to the velocity of light in glass.
n = Velocity of light in air (Va)/Velocity of light in glass (Vg)
Or
Refractive index, n is the constant number which expresses how many times or to what extent a
light ray bends when passing through different medium.
Absolute  refractive  index  (n
)  is  the  refractive  index  between  vacuum  or  air  and  any  other
a
medium.
The refractive indices between air and some common media is given below:
Medium
Refractive index (n)
Diamond
2.417
Ethanol
1.360
32



Glass (Crown)  1.520
Quartz
1.553
Water (at 20ºC0  1.333
Air (at stp)
1.00029
Example 2
The refractive index for light passing from air to water is equal to 1.333 find the refractive index
for light travelling from water to air.
Data given:
Refractive index an
of air to water = 1.333
w
Required: To find refractive index from water to air
Since
anw = 1.333
wna = (1/anw)
= (i/1.333)
: wna = 0.75
Real and Apparent Depth
Real depth
is the actual height measured without taking account any refraction of light
Apparent depth
is the virtual height measured when viewed by observer.
The Concept of Critical Angle and Total Internal Reflection of Light
Explain the concept of critical angle and total internal reflection of light
Critical angle
33



Critical angleis the angle of incidence (i) for which the angle of refraction (r) is equal to 90º . It is
obtained when light rays moves from a dense medium to a less dense medium.
For refractive index
n=Sini/sinr
But i= Critical angle, C
r = 90º
Thus n= sinC/sin 90º
n=SinC/1
n = Sin C
c= Sin -1 (n)
Total Internal Refraction
This occurs when a light ray from a less dense medium is reflected into the denser medium at the
boundary separating the two media.
Conditions for total internal reflection to occur include the following:
1.
Light must be travelling from a more dense to less dense medium.
2.
Light must incident at the boundar y at an angle gr eater than the critical angle (C).
Optical fibres
These are very thin tubes of plastic or glass and because they are so thin they can bend without
breaking, so they can carry light around the corners.
Uses of optical fibres
Used in telecommunications to carry telephone calls  over vast distance, without loss of
intensity and without interfer ence.
34



Used in endoscope to  view  inside a  patient body  for example  inside  stomach. Light  is
carried into the stomach through a bunch of fibres and is reflected into small camera, which then
displays a pictur e on a screen.
The Occurance of Mirage
Explain the occurrence of mirage
This  is  the  phenomenon  inwhich  an  object  appears  to  be  at  an  incorrect  position  due  to  the
bending of light rays from the object.
Mirages occur during hot days.
Refraction of Light by Rectangular Prism
The Passage of Light through a Triangular Prism
Trace the passage of light through a triangular prism
Deviation of light in a prism is the changing in direction of the incident ray when it enters/hits a
triangular glass prism.
Where i
is the angle of incidence
s is the angle of deviation
The minimum angle of deviation ( qm)
In order to determine the minimum angle deviating (Qm) then we must set triangular Glass prism
as follows.
35



The Dispersion of White Light
Demonstrate the dispersion of white light
Dispersion of  light is the splitting up of  light beam (white light)  into its  seven components of
colour by a prism.
Spectrum is the patch or band of colours which comprise / constitute seven component of white
light.
Pure section is the patch or band of colours in which the colours are clearly separated.
In order to produce pure spectrum then we must use two converging lenses (convex lenses).
When colours of spectrum are combined, they for m white light.
In order to combine colours of the spectrum, weneed two triangular glass prisms and one lens.
36



Impure spectrum:
the band/patch of colours which overlap and are not seen clearly.
The rainbow:
a bow-shaped spectrum of seven colours of white light formed when white light
undergoes  dispersion  within  the  rain  drops  because  water  is  denser  than  air,  so  has  a  large
refractive index.
Activity 1
A rainbow can be demonstrated as follows:
Spray some water into the air in a direction opposite to that of the sun.
Look  at the  water shower  while  you  face  away  from  the  sun.  You  will  see  the  colour of  the
spectrum of white light in the falling drops of water. The spectrum so formed hasthe shape like a
bow. So it is called rainbow.
There are two main types of rainbow:
1.
Primary rainbow
2.
Secondary rainbow
Primary rainbow
This is formed when light undergoes one or single total internal reflection in the water droplets.
In this type of the rainbow the violet colour is on the inside of the bow while the red colour is on
the outside.
The Angles of Deviation and Minimum Deviation
37



Determine the angles of deviation and minimum deviation
Finding the refractive index (n) of glass by using the deviation of light in a prism
:
Refracting angle of prism is A
Snell s law
S in i/Sin r = N
Sin i= n sin r
Sin e  = nsin i
From Geometry of figure
I = A- r
The total  angle of deviation (s) is  the  angle between the direction orf  the  incident  ray and the
emergent ray.
Again from the Geometry Q is given by:
S= i+r - A
When  the  deviation  is  a  minimum  (Sm)  the  passage  of  light  through  the  prism  will  be
symmetrical so:
I = r „and r = I
This means that;
A + Smin = 2i = 2r
Therefore;
Refractive index, n = Sin (A + Smin)/2
Sin (A/2)
Where
38



A = Apex angle ( angle of prism)
Smin – The angle of minimum deviation
A Simple Prism Binocular
Construct a simple prism binocular
Simple prism binocular
Colours of Light
The Component of White Light
Explain the component of white light
There are two types of colour of light
1.
Primary colour of light
2.
Secondary colour of light
Primary colour of light
These are basic ( fundamental ) Colour of light to which the eye is most sensitive.Primary Colour
of light Include the following
1.
Red
2.
Green
3.
Blue
Secondary colours of light
39



These are colour of light obtained after mixing primary colours of light
Colour mixing by Addition
This  is  the  process  of  combining  primary  colours  of  light  without  loss  any  colour  to  form
secondary colours of light.
Primary color  Secondary color
Red + Blue  Magenta
Red + Green  Yellow
Blue + Green  Cyan
Colours of White Light
Recombine colours of white light
When all white light ( Red , Blue and Green)Combineforms WHITE LIGHT.
Complementary  colours  of  light
:  These  are  the  colours  which  produce  white  light  when
combined.
Red + Blue+ Green - White light
Red + Cyan - White light
Blue + Yellow - White light
Green + Magenta - White light
The Appearances of Coloured Object under White Light
Explain the appearances of coloured object under white light
There are two types of coloured paints ( pigments)  which Include the following
1.
Primary coloured pigment (paints)
2.
Secondary coloured pigment (paints)
Primary, Secondary and Complementary Colours of Light
40



Identify primary, secondary and complementary colours of light
Primary Coloured pigments
These are basic coloured pigments which form secondary coloured pigment when combined.
The primary coloured pigments include:Yellow, Cyan and Magenta
Secondary colour pigments
These  are  coloured  pigments  which  are  formed  when  two  primary  colours  combine,  whichis
always accompanied with the removal of other colours.
Difference between Additive and Subtractive Combination of Colours
Distinguish between additive and subtractive combination of colours
Colour Mixing by Substration
Is  the  process  of  mixing  two  primary  coloured  paints  (  pigments)  to  f orm  secondary  colour
white.
Example 3
Magenta + Cyan
Magenta = ( Blue) + ( Red)
Cyan = (Blue) + ( green)
The colour which is common to Blue will appear while red and green disappear.
Magenta + Cyan = Blue
Example 4
Magenta + yellow
Magenta = (Blue) + (Red)
Yellow = (Green) + (Red)
The colour which is common to both red will appear while blue and green will disappear.
41



Hence
Magenta + Yellow = Red
Example 5
Cyan + yellow
Cyan = (Blue) + (Green)
Yellow = (Red) + (Green)
The colour which is common to both green will appearwhile Blue and Red will disappear
Hence
Cyan + Yellow = Green
Refraction of Light by Lenses
Difference between Convex and Concave Lenses
Distinguish between convex and concave lenses
A lens is a transparent medium bounded by two surfaces of regular shape. There are two major
categories of lenses which include:
The Terms Focal Length, Principle Focus, Principle Axis and Optical Centre
as Applied to Lenses
Explain  the  terms  focal length, principle focus,  principle axis and optical centre as applied  to
lenses
Optical center
is a geometric center of a lens.
Center of curvature
is the center of the sphere in
which a lens is a part.
Principal axis
is an imaginary line which passes through the optical center
of the lens at right angle to the lens.
Principle focus
is a point through which all rays traveling
close and parallel to the principal axis pass through.
The Focal Length of a Lens
Determine practically the focal length of a lens
42



Focal length is a distance between between optical centre and the principal focus. It is important
to note that the the principal focus is not the halfway between the optical centre and the centre of
curvature  in  lenses  as it is  in  mirrors.  The  plane through the  principal  focus  which is  at right
angles with the principal axis is called the focal plane.
Example 6
An object is 2 cm high and placed 24cm from a convex lens. An image formed 72 cm. find the
focal length of the lens.
Solution
i/f = 1/u + 1/v
1/f =1/24 + 1/72
1/f = 4/72
f = 18cm.
The Immage Formed by a Lens
Locate the image formed by a lens
Rays diagrams are normally used toillustratesthe f ormation of images by lenses.
1.
A ray parallel to the principal axis passes through or appears to diverge from the principal
focus after refraction.
2.
A ray  of  light passing  through  the principal focus  of  a  lens  is refracted  parallel  to  the
principal axis of the lens.
3.
A  ray  of  light  through  the  optical  center  of  the  lens  continues  throughundeviated(Not
change direction)
43



The position, Size and Nature of the Image formed by Lens
Determine the position, size and nature of the image formed by lens
The nature, position and size of the image formed by a lens depends on the position of the object
in  relation  to the type  of lens. For  example  in converging lens when the object  is between the
lens and principal focus the image will be formed at the same side as the object but further from
the  lens.  It  is  virtual,  erect,  and  magnified.  The  image  by  concave  lens  is  erect,  virtual  and
reduced.
Activity 2
1.
Take a convex lens. Find its approximate focal length in a way described in Activity 11.
2.
Draw  five  parallel  straight  lines,  using  chalk,  on  a  long  Table  such  that  the  distance
between the successive lines is equal to the focal length of the lens.
3.
Place the lens on a lens stand. Place it on the central line such that the optical centre of
the lens lies just over the line.
4.
The two lines on either side of the lens correspond to F and 2F of the lens respectively.
Mark them with appropriate letters such as 2F
, F
, F
and 2F
, respectively.
1
1
2
2
5.
Place a burning candle, far beyond 2F
to the left. Obtain a clear sharp image on a screen
1
on the opposite side of the lens.
44



6.
Note down the nature, position and relative size of the image.
7.
Repeat this Activity by placing object just behind 2F
, between F
and 2F
at F
, between
1
1
1
1
F
and O. Note down and tabulate your observations.
1
The nature, position and relative size of the image formed by convex lens for various positions of
the object is summarized in the table below:
Position of the object  Position of the image  Relative  size  of  the
Nature  of  the
image
image
Highly  diminished,  point-
At infinity  At focus F
sized  Real and inverted
2
Beyond 2F
Between F
and 2F
Diminished  Real and inverted
1
2
2
At 2F
At 2F
Same size  Real and inverted
1
2
Between F
and 2F
Beyond 2F
Enlarged  Real and inverted
1
1
2
Infinitely  large  or  highly
At focus F
At infinity
enlarged  Real and inverted
1
Between  focus  F
and  optical
On the same side of the lens as the
1
centre O
object  Enlarged  Virtual and erect
Activity 3
1.
Take a concave lens. Place it on a lens stand.
2.
Place a burning candle on one side of the lens.
3.
Look through the lens from the other side and observe the image. Try to get the image on
a screen, if possible. If not, observe the image directly through the lens.
4.
Note down the nature, relative size and approximate position of the image.
5.
Move  the  candle  away  from  the lens. Note the  change  in  the size  of the  image.  What
happens to the size of the image when the candle is placed too far away from the lens.
45



Nature, position and relative size of the image formed by a concave lens for various positions of
the object
Position of the object  Position of  the image  Relative  size  of   the
Nature  of  the
image
image
Highly  diminished,  point-
At infinity  At focus F
sized  Virtual and erect
1
Between  infinity  and  optical  centre  O
Between  focus  F
and  optical
1
of the lens
centre O  Diminished  Virtual and erect
The Magnification of the Lens Camera
Determine the magnification of the lens camera
As  we  have  a  formula  for  spherical  mirrors,  we  also  have  formula  for  spherical  lenses.  This
formula  gives  the  relationship  between  object  distance  (u),  image-distance  ( )  and  the  focal
length (f ). The lens formula is expressed as1/  - 1/u = 1/f(8)
The lens formula given above is general and is valid in all situations for any spherical lens. Take
proper  care  of  the  signs  of  different  quantities,  while  putting  numerical  values  for  solving
problems relating to lenses.
The magnification produced by a lens, similar to that for spherical mirrors, is defined as the ratio
of the height of the image and the height of the object. It is represented by the letter m. If h is the
height  of  the  object  and  h'  is  the  height  of  the image given  by  a lens, then the  magnification
produced by the lens is given by,m = Height of the Image / Height of the object = h' / h(9)
Magnification produced by a lens is also related to the object-distance u, and the image-distance
. This relationship is given byMagnification (m ) = h' / h =   / u(10)
Example 7
A concave lens has focal length of 15 cm. At what distance should the object from the lens be
placed so that it forms an image at 10 cm from the lens? Also, find the magnification produced
by the lens.
Solution
46



A concave lens always forms a virtual, erect image on the same side of the object.
Image-distance v = –10 cm;
Focal length f = –15 cm;
Object-distance u = ?
Since, 1 /v - 1 / u = 1 / f
or, 1 / u = 1 / v - 1 / f
1 / u = 1 / -10 - 1 / (-15) = - 1 / 10 + 1 / 15
1 / u = (-3+2) / 30 = 1 / (-30)
or, u = - 30 cm.
Thus, the object-distance is 30 cm.
Magnification m = v/ u
m = -10 cm / -30 cm = 1 / 3 = +0.33
The positive sign shows that the image is erect and virtual. The image is one-third of the size of
the object.
The  Relationship  between  Focal  Length  (f)  Object  Distance  (u)  and  Image
Distance (v) as Applied to Lenses
Determine the relationship between focal length (f) object distance (u) and image distance (v) as
applied to Lenses
The lens equation is given as 1/f =1/u + 1/v , if sign convection is used for u, v and f the equation
applies to both converging and diverging lenses for all cases of object and image.
Example 8
An object is placed 12 cm from converging lens of focal length 18 cm. Find the position of the
image.
Solution
47



Since the lens is converging f = +18 cm. 1/v = 1/18 -1/12, v = -36.
The image is virtual.
48
 

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