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    This module is included inLens: Siyavula: Physics (Gr. 10-12)
    By: Siyavula

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Introduction

The light that human beings can see is called visible light. Visible light is actually just a small part of the large spectrum of electromagnetic radiation which you will learn more about in (Reference). We can think of electromagnetic radiation and visible light as transverse waves. We know that transverse waves can be described by their amplitude, frequency (or wavelength) and velocity. The velocity of a wave is given by the product of its frequency and wavelength:

v = f × λ v = f × λ
(1)

However, electromagnetic radiation, including visible light, is special because, no matter what the frequency, it all moves at a constant velocity (in vacuum) which is known as the speed of light. The speed of light has the symbol cc and is:

c = 3 × 10 8 m . s - 1 c = 3 × 10 8 m . s - 1
(2)

Since the speed of light is cc, we can then say:

c = f × λ c = f × λ
(3)

Colour and Light

Our eyes are sensitive to visible light over a range of wavelengths from 390 nm to 780 nm (1 nm = 1×10-91×10-9 m). The different colours of light we see are related to specific frequencies (and wavelengths) of visible light. The wavelengths and frequencies are listed in Table 1.

Table 1: Colours, wavelengths and frequencies of light in the visible spectrum.
Colour Wavelength range (nm) Frequency range (Hz)
violet 390 - 455 769 - 659 ×1012×1012
blue 455 - 492 659 - 610 ×1012×1012
green 492 - 577 610 - 520 ×1012×1012
yellow 577 - 597 520 - 503 ×1012×1012
orange 597 - 622 503 - 482 ×1012×1012
red 622 - 780 482 - 385 ×1012×1012

You can see from Table 1 that violet light has the shortest wavelengths and highest frequencies while red light has the longest wavelengths and lowest frequencies.

Exercise 1: Calculating the frequency of light given the wavelength

A streetlight emits light with a wavelength of 520 nm.

  1. What colour is the light? (Use Table 1 to determine the colour)
  2. What is the frequency of the light?

Solution

  1. Step 1. What is being asked and what information are we given? :

    We need to determine the colour and frequency of light with a wavelength of λ=520λ=520 nm = 520×10-9520×10-9 m.

  2. Step 2. Compare the wavelength of the light to those given in Table 1 :

    We see from Table 1 that light with wavelengths between 492 - 577 nm is green. 520 nm falls into this range, therefore the colour of the light is green.

  3. Step 3. Next we need to calculate the frequency of the light :

    We know that

    c = f × λ c = f × λ
    (4)

    We know cc and we are given that λ=520×10-9λ=520×10-9 m. So we can substitute in these values and solve for the frequency ff. (NOTE: Don't forget to always change units into S.I. units! 1 nm = 1×10-91×10-9 m.)

    f = c λ = 3 × 10 8 520 × 10 - 9 = 577 × 10 12 Hz f = c λ = 3 × 10 8 520 × 10 - 9 = 577 × 10 12 Hz
    (5)

    The frequency of the green light is 577×1012577×1012 Hz

Exercise 2: Calculating the wavelength of light given the frequency

A streetlight also emits light with a frequency of 490×1012×1012 Hz.

  1. What colour is the light? (Use Table 1 to determine the colour)
  2. What is the wavelength of the light?

Solution

  1. Step 1. What is being asked and what information are we given? :

    We need to find the colour and wavelength of light which has a frequency of 490×1012×1012 Hz and which is emitted by the streetlight.

  2. Step 2. Compare the wavelength of the light to those given in Table 1 :

    We can see from Table 1 that orange light has frequencies between 503 - 482×1012×1012 Hz. The light from the streetlight has f=490×1012f=490×1012 Hz which fits into this range. Therefore the light must be orange in colour.

  3. Step 3. Next we need to calculate the wavelength of the light :

    We know that

    c = f × λ c = f × λ
    (6)

    We know c=3×108m.s-1c=3×108m.s-1 and we are given that f=490×1012f=490×1012 Hz. So we can substitute in these values and solve for the wavelength λλ.

    λ = c f = 3 × 10 8 490 × 10 12 = 6 . 122 × 10 - 7 m = 612 × 10 - 9 m = 612 nm λ = c f = 3 × 10 8 490 × 10 12 = 6 . 122 × 10 - 7 m = 612 × 10 - 9 m = 612 nm
    (7)

    Therefore the orange light has a wavelength of 612 nm.

Exercise 3: Frequency of Green

The wavelength of green light ranges between 500 nm an d 565 nm. Calculate the range of frequencies that correspond to this range of wavelengths.

Solution

  1. Step 1. Determine how to approach the problem :

    Use

    c = f × λ c = f × λ
    (8)

    to determine ff.

  2. Step 2. Calculate frequency corresponding to upper limit of wavelength range :
    c = f × λ f = c λ = 3 × 10 8 m · s - 1 565 × 10 - 9 m = 5 , 31 × 10 14 Hz c = f × λ f = c λ = 3 × 10 8 m · s - 1 565 × 10 - 9 m = 5 , 31 × 10 14 Hz
    (9)
  3. Step 3. Calculate frequency corresponding to lower limit of wavelength range :
    c = f × λ f = c λ = 3 × 10 8 m · s - 1 500 × 10 - 9 m = 6 , 00 × 10 14 Hz c = f × λ f = c λ = 3 × 10 8 m · s - 1 500 × 10 - 9 m = 6 , 00 × 10 14 Hz
    (10)
  4. Step 4. Write final answer :

    The range of frequencies of green light is 5,31×1014 Hz 5,31×1014 Hz to 6,00×1014 Hz 6,00×1014 Hz .

Calculating wavelengths and frequencies of light

  1. Calculate the frequency of light which has a wavelength of 400 nm. (Remember to use S.I. units)
  2. Calculate the wavelength of light which has a frequency of 550×1012550×1012 Hz.
  3. What colour is light which has a wavelength of 470×10-9470×10-9 m and what is its frequency?
  4. What is the wavelength of light with a frequency of 510×1012510×1012 Hz and what is its color?

Dispersion of white light

White light, like the light which comes from the sun, is made up of all the visible wavelengths of light. In other words, white light is a combination of all the colours of visible light.

You learnt that the speed of light is different in different substances. The speed of light in different substances depends on the frequency of the light. For example, when white light travels through glass, light of the different frequencies is slowed down by different amounts. The lower the frequency, the less the speed is reduced which means that red light (lowest frequency) is slowed down less than violet light (highest frequency). We can see this when white light is incident on a glass prism.

Have a look at the picture below. When the white light hits the edge of the prism, the light which travels through the glass is refracted as it moves from the less dense medium (air) to the more dense medium (glass).

Figure 1
Figure 1 (PG12C5_001.png)

  • The red light which is slowed down the least, is refracted the least.
  • The violet light which is slowed down the most, is refracted the most.

When the light hits the other side of the prism it is again refracted but the angle of the prism edge allows the light to remain separated into its different colours. White light is therefore separated into its different colours by the prism and we say that the white light has been dispersed by the prism.

The dispersion effect is also responsible for why we see rainbows. When sunlight hits drops of water in the atmosphere, the white light is dispersed into its different colours by the water.

Addition and Subtraction of Light

Additive Primary Colours

The primary colours of light are red, green and blue. When all the primary colours are superposed (added together), white light is produced. Red, green and blue are therefore called the additive primary colours. All the other colours can be produced by different combinations of red, green and blue.

Subtractive Primary Colours

The subtractive primary colours are obtained by subtracting one of the three additive primary colours from white light. The subtractive primary colours are yellow, magenta and cyan. Magenta appears as a pinkish-purplish colour and cyan looks greenish-blue. You can see how the primary colours of light add up to the different subtractive colours in the illustration below.

Figure 2
Figure 2 (PG12C5_002.png)

Experiment : Colours of light

Aim:

To investigate the additive properties of colours and determine the complementary colours of light.

Apparatus:

You will need two battery operated torches with flat bulb fronts, a large piece of white paper, and some pieces of cellophane paper of the following colours: red, blue, green, yellow, cyan, magenta. (You should easily be able to get these from a newsagents.)

Make a table in your workbook like the one below:

Table 2
Colour 1 Colour 2 Final colour prediction Final colour measured
red blue    
red green    
green blue    
magenta green    
yellow blue    
cyan red    

Before you begin your experiment, use what you know about colours of light to write down in the third column "Final colour prediction", what you think the result of adding the two colours of light will be. You will then be able to test your predictions by making the following measurements:

Method:

Proceed according to the table above. Put the correct colour of cellophane paper over each torch bulb. e.g. the first test will be to put red cellophane on one torch and blue cellophane on the other. Switch on the torch with the red cellophane over it and shine it onto the piece of white paper.

What colour is the light?

Turn off that torch and turn on the one with blue cellophane and shine it onto the white paper.

What colour is the light?

Now shine both torches with their cellophane coverings onto the same spot on the white paper. What is the colour of the light produced? Write this down in the fourth column of your table.

Repeat the experiment for the other colours of cellophane so that you can complete your table.

Questions:

  1. How did your predictions match up to your measurements?
  2. Complementary colours of light are defined as the colours of light which, when added to one of the primary colours, produce white light. From your completed table, write down the complementary colours for red, blue and green.

Complementary Colours

Complementary colours are two colours of light which add together to give white.

Investigation : Complementary colours for red, green and blue

Complementary colours are two colours which add together to give white. Place a tick in the box where the colours in the first column added to the colours in the top row give white.

Table 3
  magenta yellow cyan
  (=red+blue) (=red+green) (=blue+green)
red      
green      
blue      

You should have found that the complementary colours for red, green and blue are:

  • Red and Cyan
  • Green and Magenta
  • Blue and Yellow

Perception of Colour

The light-sensitive lining on the back inside half of the human eye is called the retina. The retina contains two kinds of light sensitive cells or photoreceptors: the rod cells (sensitive to low light) and the cone cells (sensitive to normal daylight) which enable us to see. The rods are not sensitive to colour but work well in dimly lit conditions. This is why it is possible to see in a dark room, but it is hard to see any colours. Only your rods are sensitive to the low light levels and so you can only see in black, white and grey. The cones enable us to see colours. Normally, there are three kinds of cones, each containing a different pigment. The cones are activated when the pigments absorb light. The three types of cones are sensitive to (i.e. absorb) red, blue and green light respectively. Therefore we can perceive all the different colours in the visible spectrum when the different types of cones are stimulated by different amounts since they are just combinations of the three primary colours of light.

The rods and cones have different response times to light. The cones react quickly when bright light falls on them. The rods take a longer time to react. This is why it takes a while (about 10 minutes) for your eyes to adjust when you enter a dark room after being outside on a sunny day.

Note: Interesting Fact :

Color blindness in humans is the inability to perceive differences between some or all colors that other people can see. Most often it is a genetic problem, but may also occur because of eye, nerve, or brain damage, or due to exposure to certain chemicals. The most common forms of human color blindness result from problems with either the middle or long wavelength sensitive cone systems, and involve difficulties in discriminating reds, yellows, and greens from one another. This is called "red-green color blindness". Other forms of color blindness are much rarer. They include problems in discriminating blues from yellows, and the rarest forms of all, complete color blindness or monochromasy, where one cannot distinguish any color from grey, as in a black-and-white movie or photograph.

Figure 3
Figure 3 (color-vision-screenshot.png)
run demo

Exercise 4: Seeing Colours

When blue and green light fall on an eye, is cyan light being created? Discuss.

Solution
  1. Step 1. Think about what happens when light hits the eyes :

    Cyan light is not created when blue and green light fall on the eye. The blue and green receptors are stimulated to make the brain believe that cyan light is being created.

Colours on a Television Screen

If you look very closely at a colour cathode-ray television screen or cathode-ray computer screen, you will see that there are very many small red, green and blue dots called phosphors on it. These dots are caused to fluoresce (glow brightly) when a beam of electrons from the cathode-ray tube behind the screen hits them. Since different combinations of the three primary colours of light can produce any other colour, only red, green and blue dots are needed to make pictures containing all the colours of the visible spectrum.

Colours of light

  1. List the three primary colours of light.
  2. What is the term for the phenomenon whereby white light is split up into its different colours by a prism?
  3. What is meant by the term “complementary colour” of light?
  4. When white light strikes a prism which colour of light is refracted the most and which is refracted the least? Explain your answer in terms of the speed of light in a medium.

Pigments and Paints

We have learnt that white light is a combination of all the colours of the visible spectrum and that each colour of light is related to a different frequency. But what gives everyday objects around us their different colours?

Pigments are substances which give an object its colour by absorbing certain frequencies of light and reflecting other frequencies. For example, a red pigment absorbs all colours of light except red which it reflects. Paints and inks contain pigments which gives the paints and inks different colours.

Colour of opaque objects

Objects which you cannot see through (i.e. they are not transparent) are called opaque. Examples of some opaque objects are metals, wood and bricks. The colour of an opaque object is determined by the colours (therefore frequencies) of light which it reflects. For example, when white light strikes a blue opaque object such as a ruler, the ruler will absorb all frequencies of light except blue, which will be reflected. The reflected blue light is the light which makes it into our eyes and therefore the object will appear blue.

Opaque objects which appear white do not absorb any light. They reflect all the frequencies. Black opaque objects absorb all frequencies of light. They do not reflect at all and therefore appear to have no colour.

Exercise 5: Colour of Opaque Objects

If we shine white light on a sheet of paper that can only reflect green light, what is the colour of the paper?

Solution
  1. Step 1. Think about what determines colour :

    Since the colour of an object is determined by that frequency of light that is reflected, the sheet of paper will appear green, as this is the only frequency that is reflected. All the other frequencies are absorbed by the paper.

Exercise 6: Colour of an opaque object II

The cover of a book appears to have a magenta colour. What colours of light does it reflect and what colours does it absorb?

Solution
  1. Step 1. What colours make magenta? :

    We know that magenta is a combination of red and blue primary colours of light. Therefore the object must be reflecting blue and red light and absorb green.

Colour of transparent objects

If an object is transparent it means that you can see through it. For example, glass, clean water and some clear plastics are transparent. The colour of a transparent object is determined by the colours (frequencies) of light which it transmits (allows to pass through it). For example, a cup made of green glass will appear green because it absorbs all the other frequencies of light except green, which it transmits. This is the light which we receive in our eyes and the object appears green.

Exercise 7: Colour of Transparent Objects

If white light is shone through a glass plate that absorbs light of all frequencies except red, what is the colour of the glass plate?

Solution
  1. Step 1. Think about how light is transmitted :

    Since the colour of an object is determined by that frequency of light that is transmitted, the glass plate will appear red, as this is the only frequency that is not absorbed.

Pigment primary colours

The primary pigments and paints are cyan, magenta and yellow. When pigments or paints of these three colours are mixed together in equal amounts they produce black. Any other colour of paint can be made by mixing the primary pigments together in different quantities. The primary pigments are related to the primary colours of light in the following way:

Figure 4
Figure 4 (PG12C5_003.png)

Note: Interesting Fact :

Colour printers only use 4 colours of ink: cyan, magenta, yellow and black. All the other colours can be mixed from these!

Exercise 8: Pigments

What colours of light are absorbed by a green pigment?

Solution
  1. Step 1. Think about what colour is reflected :

    If the pigment is green, then green light must be reflected. Therefore, red and blue light are absorbed.

Exercise 9: Primary pigments

I have a ruler which reflects red light and absorbs all other colours of light. What colour does the ruler appear in white light? What primary pigments must have been mixed to make the pigment which gives the ruler its colour?

Solution
  1. Step 1. What is being asked and what are we given? :

    We need to determine the colour of the ruler and the pigments which were mixed to make the colour.

  2. Step 2. An opaque object appears the colour of the light it reflects :

    The ruler reflects red light and absorbs all other colours. Therefore the ruler appears to be red.

  3. Step 3. What pigments need to be mixed to get red? :

    Red pigment is produced when magenta and yellow pigments are mixed. Therefore magenta and yellow pigments were mixed to make the red pigment which gives the ruler its colour.

Exercise 10: Paint Colours

If cyan light shines on a dress that contains a pigment that is capable of absorbing blue, what colour does the dress appear?

Solution
  1. Step 1. Determine the component colours of cyan light :

    Cyan light is made up of blue and green light.

  2. Step 2. Determine solution :

    If the dress absorbs the blue light then the green light must be reflected, so the dress will appear green!

Figure 5

End of Chapter Exercises

  1. Calculate the wavelength of light which has a frequency of 570×1012570×1012 Hz.
  2. Calculate the frequency of light which has a wavelength of 580 nm.
  3. Complete the following sentence: When white light is dispersed by a prism, light of the colour ? is refracted the most and light of colour ? is refracted the least.
  4. What are the two types of photoreceptor found in the retina of the human eye called and which type is sensitive to colours?
  5. What color do the following shirts appear to the human eye when the lights in a room are turned off and the room is completely dark?
    1. red shirt
    2. blue shirt
    3. green shirt
  6. Two light bulbs, each of a different colour, shine on a sheet of white paper. Each light bulb can be a primary colour of light - red, green, and blue. Depending on which primary colour of light is used, the paper will appear a different color. What colour will the paper appear if the lights are:
    1. red and blue?
    2. red and green?
    3. green and blue?
  7. Match the primary colour of light on the left to its complementary colour on the right:
    Table 4
    Column AColumn B
    redyellow
    greencyan
    bluemagenta
  8. Which combination of colours of light gives magenta?
    1. red and yellow
    2. green and red
    3. blue and cyan
    4. blue and red
  9. Which combination of colours of light gives cyan?
    1. yellow and red
    2. green and blue
    3. blue and magenta
    4. blue and red
  10. If yellow light falls on an object whose pigment absorbs green light, what colour will the object appear?
  11. If yellow light falls on a blue pigment, what colour will it appear?

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