LIGHT PART II
Refraction through Prism
Prism is a solid piece of glass or transparent material that has at least two planes inclined toward each other through which light is refracted.
Types of prism
- Rectangular prism
- Triangular prism
- Rectangular prism
Rectangular prisms are commonly called glass blocks
Triangular prism
Is a wedge-shaped piece of glass material or any other transparent material. See the fig. below
Apex =The point at which two refracting surfaces of the prism meet is called the refracting edge
Triangular prism has two refracting surfaces.
Rays leaving the prism is called emergent ray
Rays entering the prism is called incident ray
Apical angle is the angle between the refracting surfaces (See the fig below)
Angle of Deviation, D
Is the angle formed by the intersection of the incident ray direction and the emergent ray direction.(see the fig below)
Consider the diagram below
From Snell’s Law
1 and 
…………..2
Therefore: 𝒂 + 𝒃 = 𝑫…………….. (i) (sum of two opposite interior angles)
𝒃𝒖𝒕…… .𝒊 = 𝒂 + 𝒓 → 𝒂 = 𝒊 − 𝒓 𝒂𝒏𝒅 𝒓𝟏 = 𝒃 + 𝒊𝟏 → 𝒃 = 𝒓𝟏 − 𝒊𝟏 𝑡ℎ𝑒𝑛, 𝑫 = 𝒂 + 𝒃 = (𝒊 − 𝒓) + (𝒓𝟏 − 𝒊𝟏)……………(ii)
Since: A and A1 is supplementary to each other → A + A1 = 180° ……(ii)
But: r + i1 + A1 = 180°…………………(iii) (sum of interior angles of a ∆) Compare equation (ii) and (iii)
r + i1 + A1 = A + A1 → 𝑨 = 𝒓 + 𝒊𝟏 → 𝒓 = 𝑨 − 𝒊𝟏 ………(iv)
Then substitute, equation (iv) into (ii)
𝑫 = (𝒊 − 𝒓) + (𝒓𝟏 − 𝒊𝟏) → 𝑫 = 𝒊 − ( 𝑨 − 𝒊𝟏)+ (𝒓𝟏 − 𝒊𝟏) 𝑫 = 𝒊 − 𝑨 + 𝒊𝟏+ 𝒓𝟏 − 𝒊𝟏 = 𝒊+ 𝒓𝟏 − 𝑨
∴ The angle of Deviation is given by: 𝑫 = 𝒊+ 𝒓𝟏 − 𝑨
The angle of deviation depends on
- The apical angle of the prism, A
- The Angle of incidence, i
- The refractive index of the glass prism.
NB:
Angle of deviation decreases with an increase in the angle of incidence and vice versa
Minimum Angle of Deviation, 
Is the deviation angle occurs when the emergent ray is refracted at an angle equal to the angle of incidence. (Consider the fig below)
and 
Substitute: 
and 
From: Snell’s law
𝒂𝝁𝒈 = 𝒔𝒊𝒏𝒊
𝒔𝒊𝒏𝒓 = 𝑺𝒊𝒏 (𝑫𝒎𝒊𝒏+𝑨𝟐)
𝑺𝒊𝒏 (𝑨𝟐)
Consider the graph below shows the relationship between i and D, for which the angle of deviation is obtained
Dispersion of white light
Dispersion of white light is the splitting of white light beam into its component colours.
This band of colours produced is called Spectrum.
The process of splitting white light into its component colors is called Dispersion.
Diagram:
Types of white Colour
Polychromatic light
Monochromatic light
Polychromatic Light
Is the colour which consists of more than one color. Example, sunlight
Monochromatic Light
Is the light which consists of only one color. Example, red colour NB:
Spectrum of colour (red, orange, yellow, green, blue, indigo and violet) is abbreviated as ROYGBIV .And each of these colours has a different wavelength.
These coloured lights are refracted differently on passing through the prism
The velocity of light in a medium (refractive index) depends on the wavelength of incident light. As a result different wavelengths are refracted by different amounts.
White colour split due to difference in wave length. Shorter wavelengths have higher refractive indices and get bent more than longer wavelengths
Wavelengths of the Colours of White Light
|
S/N |
Colour |
Wavelength (nm) |
|
1 |
Red |
625 – 740 |
|
2 |
Orange |
590 – 625 |
|
3 |
Yellow |
565 – 590 |
|
4 |
Green |
520 – 565 |
|
5 |
Blue |
440 – 520 |
|
6 |
Indigo |
420 – 440 |
|
7 |
Violet |
380 – 420 |
Types of Spectra
Pure Spectra
Pure spectrum is the one in which the colours are clearly separated from each other Impure Spectra
Impure spectrum is the one in which the colours not clearly separated from each other
Recombining Colours of Light
Spectrum comes from white light can recombine to form white colour.
Also Newton’s colour disc is used to recombine the colours.
The disc consists of sectors painted with different colors of the spectrum
When the disk is allowed to spin about its axis at very high speed, all the colors of the spectrum recombine to form white light. When it is slowed down, the individual colors of the spectrum are seen again
Newton’s color disk
The Rainbow
The rainbow is a natural phenomenon of dispersion of sunlight by raindrop.
Formation of a Rainbow
It is formed by dispersion of sunlight by drops of rain.
Since water is denser than air the dispersion of sunlight on a drop of water is the same as when it falls on a glass prism.
The light is first refracted as it enters the surface of the raindrop, reflected off the back of the drop and again refracted as it leaves the drop. (See the fig below)
Types of Rainbow
- primary rainbow
- secondary rainbow
Primary Rainbow
It is formed when light undergoes one total internal reflection (refracted twice and reflected once) in the water drops.
The violet colour is inside and the red in the outside the bow. It is formed between 400 and 420 from anti-solar point
Anti-solar point Is a point that lies directly opposite the sun from the observer, that is, on the line from the sun through the observer.
Secondary Rainbows
It is formed when light undergoes two total internal reflections in the water drops.
The violet colour is outside and the red colour is inside the bow.
Colour
Colour is the property of light that reaches our eyes.
Appearance of coloured objects under white light
The object seems to have kind of colour due to the fact that it absorbs all colours and reflect the colour that the object has.
Example
Yellow flower is yellow because it absorbs all the other colours in the light and reflects only yellow colour.
Blue object absorbs the entire colour in white light except blue.
Appearance of white objects under coloured light
When a coloured object is viewed under a coloured light, it takes the colour of that light.
Example:
The object will appear blue in blue light and red in red light. A colour filter is working on this principle.
Colour filters
Are materials made of glass or celluloid that let through light of certain colours only.
Example: Green filters allow green colour to pass through.
The colour of an object depends on the colour of the light falling on it and the colour(s) it absorbs or reflects.
Appearance of a white object to coloured light
|
White object |
coloured light |
Colour of object |
|
White object |
Red filters |
Red colour |
|
White object |
Yellow filters |
Yellow colour |
|
White object |
Green filter |
Green colour |
|
White object |
Blue filter |
Blue colour |
Types of Colour
- Primary colour
- Secondary colour
Primary colour
Primary colour is a colour that cannot be created by mixing other colours. Example, red, blue and green
Secondary colour
Secondary colour is a colour created by mixing other colours. Example, cyan, magenta and yellow
Complementary Colour
Is the colour that when mixed in a definite ratio produce white (required) colour. Consider the figure below
NB:
From the figure above
When mixing the primary colors (red, blue and green), a white color is obtained That is: Red + Blue + Green = White
When mixing two of the primary colors produces a secondary color .That is
- Green + Blue = Cyan (GBC)
- Green + Red = Yellow (GRY)
- Red + Blue = Magenta (RBM)
When mixing two of the secondary colors, white light is produced
That is: Yellow + Magenta = Magenta + Cyan = Cyan + Yellow = White color
We are only concerned with colours of light and not with coloured substances (pigments)
The complementary colour of white light is green, red and blue The complementary colour of yellow light is green and red.
Additive and subtractive mixing of colours
Additive mixing of Colours
Is the mixing of coloured light
The more colours you add, the closer the result draws to white. Therefore, mixing of coloured lights
Additive mixing of colours deals with primary colour of light colour (Red, Green and Blue) not primary colour of pigments (paints and dyes)
Adding different colours of light together increases the number of wavelengths present
Subtractive mixing of pigments
Is the mixing of colours of different paints (pigments)
Pigments: These are substances which give color to paints by reflecting light of certain colors only and absorbing all other colors.
Mixing different paints results in a darker colour because most of the light wavelengths are absorbed
Mixing two primary pigments produces a secondary pigment .That is
- cyan + magenta = blue (CMB)
- magenta + yellow = red (MYR)
- yellow + cyan = green (CYG)
The pigments act as filters that subtract one or more colours from the visible spectrum Blue, Red and Green are, therefore, the secondary pigments.
Subtractive complementary colours combine to produce BLACK. That is Blue + Green + Red = Black (See the fig below)
N B:
Each primary pigment absorbs one primary colour:
- Yellow absorbs blue and reflects red and green
- Magenta absorbs green and reflects blue and red
- Cyan absorbs red and reflects green and blue.
A secondary pigment absorbs two primary colours and reflects one:
- Red absorbs green and blue and reflects red.
- Green absorbs red and blue and reflects green.
- Blue absorbs – red and green and reflects blue.
The primary pigments are the secondary colours of light and the secondary pigments are the primary colours of light.
If you mix a primary pigment with a secondary pigment you get total absorption (black). ie Blue + Yellow = Black
The primary pigments are the complementary colours of the three primary colours of light.
Example:
A plant with green leaves and red flowers is placed in: (a) Green (b) Red (c) Blue light
ANS:
(a) In Green light |
(b) In Red light |
(c) In Blue light |
|
Green leaves will appear green Red flowers will appear black |
In red light Green leaves will appear black Red flowers will appear red |
In blue light Green leaves will appear black Red flowers will appear black |
Why red light is used for danger signals?
ANS: Because red light is scattered the least by air molecules due to its highest wavelength so it is able to travel the longest distance through fog, rain and alike
A red bus with blue letter on its stops in front of a yellow light at right. Describe the appearance of the bus ANS: In yellow light
The red bus will appear red because yellow is composed of green and red
The blue letters will appear black
Class Activity – 4
Explain what is meant by a spectrum .Describe with the aid of a diagram how would you obtain the spectrum of white light
Distinguish between a pure and an impure spectrum. Explain with the aid of a diagram how a pure spectrum can be produced in the laboratory .How are the colours of the spectrum recombined?
A beam of white light is allowed into a dark room through a hole .In the dark room ,the beam falls on a white screen .How will the screen appear if: a piece of red glass is placed in the path of the beam (b) a piece of green glass is placed between the screen and the red glass?
Explain, giving examples , what is meant by: (a) additive combination of colours (b) subtractive combination of colours 5 Why does an object appear coloured when light falls onto it? Explain, giving examples, what is meant by primary, secondary and complementary colours.
A flag has a green disc on a yellow background .How will the flag appear in: (a) green light (b) red light (c) blue light
State , giving a reason for each answer, the colour that results when:
(a) a blue light and a yellow light are mixed (b) blue paint and yellow paint are mixed
What color would be seen if white light is viewed through: (a) a red filter? (b) a cyan filter? (c) an orange filter?
A book which looks red in white light is viewed in magenta light. In what color does it appear?
White light is viewed through a combination of a yellow filter and a red filter held in contact. What color is seen
Explain the meaning of the term ‘’dispersion’’ of white
Explain why the result of mixing blue and yellow paints is very different from that of mixing blue and yellow lights
A painter has a blue – green (cyan) paint which she wants to make pure green. What color pigment should she add to the paint? Explain your answer
Briefly explain, why the sky looks blue?
Under pure yellow light what will be the appearance of the blue piece of cloth?
Danger signs along the road as well as tail and brake lamps of motor vehicles rear are painted red. Briefly explain the reason behind.
Explain each of the following:– (a) The appearance of a blue flag when viewed in day light through a sheet of red glass (b) The appearance of a red flag with green stripes when viewed in day light through a sheet of green glass (c) The appearance of a man wearing blue shirt and red trousers, holding a handkerchief of green color when viewed in the pure yellow light
