Wave: Light Around Us, Denser and Rarer Medium

Lean a pencil in a glass that is half full of water and look at it from the side. The pencil seems to break or bend exactly where it enters the water. Pull it out and it is perfectly straight. Nothing happened to the pencil. What changed is the path of the light travelling from the pencil to your eyes.

The surface where two different media meet is called an interface. Here the interface is the top surface of the water, the borderline between water and air. Light travels at one speed in water and at a different speed in air. When light crosses from one medium into the other, its speed changes, and so does its direction. Because of this, our eyes see the part of the pencil under the water a little higher than where it really is, and the pencil seems to break at the interface.

Stir a glass of water hard, or pour out some soda water, and air bubbles rise through it. Seen from the side, some of the bubbles shine like tiny silver beads. They shine in just the way a mirror shines when light is reflected from its surface.

Inside the water, light heading towards a bubble has to pass from water into air. At the outer surface of the bubble, this light is reflected back into the water instead of passing into the air. When that reflected light reaches our eyes, the bubble looks bright and silvery.

The same behaviour of light is used in optical fibres. An optical fibre is a very thin, flexible thread of glass or plastic. It is constructed on the principle that light going from one optical medium towards another optical medium is reflected into the same medium. So light sent into one end keeps bouncing along inside the fibre until it comes out at the far end, even where the fibre bends. Optical fibres carry internet and telephone signals over long distances.

Hold a hand lens over a newspaper and the letters look much bigger than they really are. The light coming from the letters passes through the glass of the lens before it reaches your eye. The glass used in a hand lens has a special structure: it is thicker in the middle and thinner towards the edges. This shape changes the path of the light, so the letters appear large when they are viewed through the lens.

After rain, with the sun shining from behind you, a rainbow may appear in the sky. During the formation of a rainbow, sunlight splits into its seven constituent colours: violet, indigo, blue, green, yellow, orange and red. The white-looking light of the sun is really these seven colours together.

To see the seven colours of a rainbow, our eyes play an important part. The cone cells found in the inner layer of the eye let us tell one colour from another. A rainbow is also a far object, a long way from us. We are able to see distant objects like a rainbow and nearby objects like the page of a book because each of our eyes has a natural lens, similar to a hand lens.

The lens of the eye can change its thickness, and that is how we see both far and near objects clearly. Sometimes, though, vision becomes blurred. There are two main reasons:

• The eye is unable to change the thickness of its lens.
• The lens loses its transparency, so light can no longer pass through it clearly.

So some people cannot see distant objects distinctly, some cannot see nearby objects distinctly, and some are not able to distinguish colours. The problem of not seeing distant or nearby objects is solved by getting the eyes checked and wearing spectacles with lenses of suitable power.

The light from every object we look at reaches us through transparent media. Some of these media are natural, like air and water. Others are artificial, like the glass of a window or of a pair of spectacles.

Light does not travel equally fast in all of them. The table below gives the speed of light in six media.

Reading down the table, the speed only falls. Among the given media, light is fastest in air, at \( 3.00 \times 10^{8} \) m/s, which means three hundred million metres every second. It is slowest in diamond, at \( 1.24 \times 10^{8} \) m/s.

Because the speed of light differs from one medium to another, media can be sorted into two kinds. The sorting is always done for a pair of media. Only by comparing the speed of light in the two do we decide which one is denser and which one is rarer.

Take the pair air and glass. The speed of light is \( 3.00 \times 10^{8} \) m/s in air and \( 2.00 \times 10^{8} \) m/s in glass. Light is slower in glass, so in this pair glass is the denser medium and air is the rarer medium.

Worked example: in the pair alcohol and glass, which is the denser medium?

Step 1: Reading the speed of light in alcohol from the table:

\[ 2.19 \times 10^{8}\ \text{m/s} \]

Step 2: Reading the speed of light in glass from the table:

\[ 2.00 \times 10^{8}\ \text{m/s} \]

Step 3: Comparing the two speeds, which have the same power of ten, by their first numbers:

\[ 2.00 \times 10^{8} < 2.19 \times 10^{8} \]

Step 4: Deciding from the comparison. Light is slower in glass, so in this pair glass is the denser medium and alcohol is the rarer medium.

Denser and rarer are words of comparison, not fixed labels. Water is denser than air, because light is slower in water than in air. The same water is rarer than glass, because light is faster in water than in glass. So before calling a medium denser or rarer, always say which pair you mean.

The word dense can mislead. A physically denser substance has more mass packed into the same volume, and a liquid of lower density floats on one of higher density. Optical density is a different idea. It only tells us how slowly light travels in a medium.

Kerosene oil floats on water, which means the physical density of kerosene oil is less than that of water. Now compare the speed of light: \( 2.08 \times 10^{8} \) m/s in kerosene oil and \( 2.25 \times 10^{8} \) m/s in water. Light is slower in kerosene oil, so kerosene oil is optically denser than water. A medium can be optically denser and still physically lighter. A medium with higher optical density is not necessarily physically denser.

There is another way to tell the denser and rarer medium apart, even without a table. When light passes from one medium into another, its direction changes. This change in the direction of a light ray when the medium changes is the refraction of light, and the way the ray turns shows which medium is denser and which is rarer.