Through the looking glass
In December 2013, the 68th Session of the UN General Assembly proclaimed 2015 as the International Year of Light and Light-based Technologies (IYL 2015). Thus 2015 is a great year to begin, or add to, activities about light that can be conducted in a classroom.
Here are two articles on optics where we look at some history and then get down to some experiments to understand the basic ideas behind light.
History of science through an optical lens
Pinaki Das
Why history of science
Textbooks usually present science as a “finished product” rather than as a “work in progress”. How did the ideas take shape? What were the contending theories? These are never discussed. An important part of learning is to learn how others have thought about the problem. Thus history of science seems to me to be an integral part of the teaching of science. I have delved into the history of science looking for the “connections” which are sadly missing from our textbooks. Here I present some random notes in the history of the development of optics.
How do we see?
This is the question that we usually start with. Almost everyone in the classroom agrees that light from some source falls on the object and gets reflected on the eye. There are exceptions and I remember a dissenting voice which thought that light from our eyes fell on the object and made it visible. Everyone laughed, but I later learnt that this was indeed the way the Greek philosophers thought about light and vision. For the Greeks it was the eye which sent a ray of light to the object seen. We know that Perseus armed himself with a mirror to avoid the malevolent rays that emanated from the eyes of the gorgon Medusa. History of science shows how commonsense is related to the leading scientific ideas of the times; what we think as “obvious” is a result of our constant exposure to our scientific and cultural environment.
Rectilinear propagation and the law of reflection
Euclid of Alexandria who gave us our geometry also gave us ray optics. Nowadays we justify the idea of representing light as a ray and prove that it travels in straight lines by pointing to common everyday experiences – e.g. the fact that we cannot see things round the corner or that shadows are cast. But the Greeks deduced both the properties of rectilinear propagation and the law of reflection from the postulate that sight should reach the object to be seen as quickly (least distance, not time) as possible (Hero of Alexandria/Damianus, 4th century AD). The law of reflection can be easily established empirically. But to go beyond a law and gain a deeper insight – a higher ground – from where the law itself can be derived is a great step in science. At the same time it reveals the inter-relation between mathematics and physics: as Galileo famously said, “…the great book of Nature … is written in mathematical language.”
Refraction and the speed of light
It is well known that, in general, Greek ideas in science have reached us through the Arabs. But in optics, the Arab contribution is fundamental. It was al-Haytham (Basra/Cairo 965-1039AD) who gave us the modern notion that light travels from the object to the eye. He reversed the direction of propagation of light and in the process entirely recast the science of optics. The ability of the eye to instantly see different objects at different distances no longer required light to travel at infinite speed. al-Haytham was the first to connect the phenomenon of refraction to the speed of light in different media. This connection finally found expression 600 years later with Fermat (1650) who deduced the law of refraction from the postulate of path of least time. Light, in going from one media to another, underwent an abrupt change of direction (refraction) and violated the shortest distance hypothesis which is a straight line. Fermat replaced the Greek notion of ‘path of least distance’ by the postulate of “path of least time” and derived Snell’s law. Snell’s law (1620) which was derived empirically did not provide any insight into the nature of light.
Astronomy, navigation and the speed of light
The problem of the apparent position of stars due to atmospheric refraction has troubled astronomers from ancient times. By the time Snell discovered the sine law it was of little practical value as the astronomers from Ptolemy to Tycho Brahe had already prepared detailed refraction tables to enable better observation of stellar/ planetary positions. Kepler who is regarded as the father of modern optics explained perfectly the working of all optical instruments even before the discovery of Snell’s law which he himself came very near to discovering.
In 1676 Ole Roemer, a Dutch astronomer – searching for a dependable clock in the skies – gave us the first measurement of the speed of light. The navigators were in dire need of determining the longitude of a place accurately. Determining longitude is simply a matter of knowing the difference of time at two places, but the clocks of the day were not sufficiently accurate. Some celestial event occurring daily at the same time could be observed by navigators to set their clocks. Such an event visible everywhere is the eclipse of Io, one of the four large moons of Jupiter discovered by Galileo in 1610. Roemer’s discovery brought an end to a 2000 year old controversy about whether the speed of light was finite or was it “instantaneous” as the ancients believed.
It must be understood that the measurement of the speed of light was the key to the understanding of the nature of light. In 1850 Foucault successfully demonstrated that light travels slower in water as compared to air as predicted by the wave theory of light. In 1865 Maxwell predicted that a combination of electric and magnetic fields would propagate through space at a speed of 3×108 m/s. Considering that Maxwell derived this speed from the ratio of certain electrical and magnetic units, the coincidence of the theoretical speed of electro-magnetic waves with the observed speed of light was taken as an indication that light was an electro-magnetic wave.
Lens, telescope and Galileo: the birth of modern astronomy
The revolutions in science are either concept driven or driven by new tools. The telescope (lens) and the spectroscope (prism) are two such tools that revolutionized science. Since the lens and prism are taught in high school in some detail, it seems necessary to me to put these tools in the proper perspective when we discuss their working in class.
In 1610 Galileo revolutionized astronomy when he pointed his lenses (the telescope) at the sky. The moons of Jupiter that he observed represented a miniature solar system and helped substantiate the heliocentric theory of Copernicus. The next great step was taken in 1666 by Newton – when he proved that the prism breaks up white light into its constituent colours. He disproved the millennium old idea that it was the prism that somehow added colour to the sunlight passing through it.
Prism, spectroscope, and Fraunhofer: the birth of Astrophysics
But the real significance of Newton’s discovery came to be realized much later when in 1814 Fraunhofer looked at starlight through a prism and laid the groundwork for modern astrophysics. He combined the lens (telescope) and the prism to make a spectroscope and on examining sunlight, found the spectrum crossed by hundreds of dark lines. On examining light from other stars he found different bands of dark “fraunhofer lines”. When he examined the spectrum from flames in his laboratory he found the same lines but instead of appearing dark (as in the case of the sun) they appeared bright. Fraunhofer died before he could solve his own puzzle, and without realizing that his results established a connection between the elements that existed in the sun and on earth. His work eventually led to momentous discoveries in stellar spectroscopy; the composition of stars to the expanding universe – none would be possible without the prescient discoveries of Fraunhofer and his prism.
Points to ponder or discuss
1. Can we prove the law of reflection by assuming that light takes the least path?
2. Why is it that Newton failed to see what Fraunhofer saw? Both examined sunlight with a prism.
Bibliography
1. Mathematical methods in Science, George Polya; The Mathematical Association of America, 1977
2. Astronomy, (ed) Rapport and Wright, Washington Square Press, 1965
3. The Feynman Lectures on Physics, Vol 1
4. Physics-Foundations and Frontiers, George Gamow and J M Cleveland, Prentice-Hall, 1960
5. A History of scientifi c Thought, (Ed.) Michel Serres, Blackwell 1995
Learning principles of optics through simple experiments
HC Verma
Light has been my favourite topic all-time. While humans, animals, and birds directly use light to experience the thrill of this wonderful world, even plants look to light for their survival and growth through photosynthesis.
At school level we are told mostly about four major behaviours of light.
• It moves in a straight line making shadows of obstacles in between
• It reflects from smooth surfaces allowing us to comb our hair in front of mirrors
• It refracts allowing us to make cameras, telescopes, and microscopes
• It comes with different colours making things look colourful and making beautiful rainbows
There are many more exciting things about light and the 2014 Nobel Prize for blue LED is a testimony. But even the above four are very interesting and you can have a lot of fun with these. Here are some fun-activities based on these behaviours of light. I am also floating some questions which can be used to trigger a useful brainstorming.
What is the shape of the hole? (Rectilinear propagation)
A is a cardboard sheet and B is a white screen. Cut a hole of about 1 cm linear size in cardboard A. The shape of the hole is your choice. Suppose you make a square hole. Put an electric bulb in front of the hole at a distance of, say 20 cm. Place the screen B on the other side of the cardboard A at a distance of about 10 cm. Light going through the hole will fall on screen B and the shape of the patch of light will be similar to the shape of the hole. This fits well with the rectilinear propagation of light. Now shift the screen away from the hole and look at the light patch on the screen. See how the shape of the patch changes with the distance between the screen and the hole. Make another hole of a different shape, say, triangular and repeat. You will be amazed to see that when the separation between the hole and screen is large, the shape of the hole becomes almost irrelevant.
Try and analyze this result with rectilinear propagation of light.
How does light travel in a bent tube? (Reflection)
Take a thin plastic tube. I generally use the drip tube used in hospitals. Cut about 10 cm of the tube. Send a light from a red laser pointer into one end of this tube. Bend the tube in the shape of a circular arc or any other curved shape. Does light travel along the bent tube? Do you see a red light at the other end of the tube? Does it go into the wall of the tube and bend along with the tube? The light indeed travels in a straight line. It seems to go along the bent tube due to multiple reflections from the tube surface, each reflection obeying the law of reflection. Is it an example of total internal reflection? Why am I suggesting a laser light instead of a usual torch?
Why does a pencil in water seem straight to me but broken to you? (Refraction)
You must have seen diagrams in textbooks where a pencil is partially dipped in water. The pencil is kept at an angle with the vertical and seems to bend at the water surface when viewed from outside. The explanation is simple. As you see from above, the parts of the pencil inside water appear to be lifted making it look bent.
More interesting is to put the pencil vertically in water in a rectangular glass vessel and view it sideways. Keep your eyes at a position where the line joining the pencil to the eye is perpendicular to the glass surface in front. The pencil looks straight and intact. Now shift your eyes left and see that the pencil looks broken. The parts inside and outside water are parallel but not in the same line.
Explain in terms of refraction from water to glass to air.
Putting the pencil in a rectangular vessel in an inclined position also gives interesting views. Watch from different positions. You will get various images, sometimes three or more images.
Why does a lens produce a coloured image of a white light bulb (chromatic aberration)
Normally, prisms are supposed to split white light into its colour components. But a lens can also do it and it is easy to see. In fact you can observe more interesting phenomena of colour separation with a lens as compared to a prism.
Take a magnifying glass of somewhat bigger aperture, 10-12 cm. Paste a black paper on its glass to block the central part, leaving only a thin periphery of say 1 cm width.
Place the lens in a vertical stand and put a bulb at about 1.2 to 1.4 times of the focal length from the lens. On the other side, put a white screen close to the lens and gradually take it away. Initially you will see a bright illuminated circular patch on the screen. As you take the screen away, the size of this circular patch will decrease. Stop when the patch is about 1-2 cm in diameter. Do you see colours appearing on the patch? You will be able to see a reddish outer periphery of the patch and bluish inner portion. In between you will find yellow. These three colours are easily visible. Shift the screen further away till you have the smallest patch on the screen. Shift it further away and the patch will spread out. Stop when the patch size is 1-2 cm. Now you see a bluish periphery and a reddish inner part. In between, yellow dominates.
So what creates such coloured patterns? It comes from dispersion. Different colours have different wavelengths and hence the glass used in the lens has different refractive indices for them. This results in different focal lengths for different colours.
The red component has the largest focal length and blue has the smallest (More correctly it should be violet but the intensity is much weaker for violet and is hidden in blue).
I have described just four simple-to-arrange experiments to demonstrate the four basic behaviours of light. You can design many more such experiments and enjoy the world of light.
Pinaki Das teaches physics at Vidyaranya High School for Boys and Girls, Hyderabad. He can be reached at pinakidas15756@gmail.com.
HC Verma is professor of physics at IIT, Kanpur and an all time physics student. He can be reached at hcverma@gmail.com.
