Light

Key points

3.2.1 Reflection of light

• The normal is a line drawn at right angles (90°) to a surface, at the point where a ray meets the surface. Draw it as a dashed line.
• The angle of incidence, i, is the angle between the incoming (incident) ray and the normal.
• The angle of reflection, r, is the angle between the reflected ray and the normal.
• Law of reflection: the angle of incidence is equal to the angle of reflection, i = r.
• Always measure these angles from the normal, not from the mirror.
• How a plane mirror forms an image: rays of light from a point on an object hit the mirror and reflect. The reflected rays spread out. When they enter your eye, they seem to come from a point behind the mirror. The image is at that point.
• No light really travels behind the mirror. The rays only seem to come from the image. So the image is virtual.
• The image in a plane mirror is:
  • the same size as the object
  • the same distance behind the mirror as the object is in front of it
  • virtual (it cannot be caught on a screen)
  • upright.
• Extra detail: the image is also laterally inverted. Left and right are swapped, as when you raise your right hand and your image raises its left hand.
• Construction to find the image of a point object O in a plane mirror and draw a ray that reaches an eye E. Extended
  1. Draw the mirror as a straight line. Mark O and E.
  2. From O, draw a line at right angles to the mirror. Continue it behind the mirror as a dashed line.
  3. Measure the distance from O to the mirror. Mark the image I on the dashed line, the same distance behind the mirror.
  4. Draw a straight dashed line from I to E. The point where it crosses the mirror is M. This is where the ray reflects.
  5. Draw the real ray as a solid line from O to M, and from M to E. Add arrows to show the direction of the light.
  6. Check: draw the normal at M. Measure i and r with a protractor. They should be equal.
• Calculations: if a ray makes an angle θ with the mirror surface, then i = 90° − θ. The angle between the incident ray and the reflected ray is i + r = 2i. Extended

3.2.2 Refraction of light

• Refraction is the change in direction of light when it passes at an angle from one transparent material into another. It happens because the speed of light changes.
• The angle of refraction, r, is the angle between the refracted ray and the normal.
• Light going from air into glass or water slows down. It bends towards the normal. So r is smaller than i.
• Light going from glass or water into air speeds up. It bends away from the normal.
• A ray that meets the boundary along the normal (i = 0°) does not change direction. Its speed still changes.
• Experiment to show refraction:
  1. Put a glass or plastic block on paper. Draw round it.
  2. Shine a narrow ray of light from a ray box at the block, at an angle to the surface. (You can use optical pins instead of a ray box.)
  3. Mark the ray going in and the ray coming out with small crosses.
  4. Remove the block. Join the crosses to draw the ray inside the block.
  5. Draw the normal at each point where the ray crosses a surface. Measure i and r with a protractor.
  6. Repeat for different angles of incidence, and with blocks of different shapes: rectangular, semicircular and triangular (a prism).
• With a rectangular block, the ray that comes out is parallel to the ray that went in. It is shifted sideways.
• With a semicircular block, aim the ray at the centre of the flat face, through the curved side. It meets the curved side along the normal, so it does not bend there. This lets you study what happens at the flat face only.
• Internal reflection: light inside glass or water meets the boundary with air. Some light is always reflected back inside.
• The critical angle, c, is the angle of incidence inside the glass (or water) at which the angle of refraction is exactly 90°. The refracted ray then travels along the boundary.
• As the angle of incidence inside the glass increases:
  • i less than c: some light refracts out into the air and some is reflected inside. As i gets closer to c, the refracted ray gets weaker.
  • i equal to c: the refracted ray travels along the boundary.
  • i greater than c: no light leaves. All the light is reflected inside. This is total internal reflection.
• Total internal reflection needs two conditions:
  • the light is travelling from glass or water towards air (from a slower material to a faster one), and
  • the angle of incidence is greater than the critical angle.
• Experimental example: use a semicircular glass block and a ray box. Slowly increase the angle of incidence at the flat face. The refracted ray gets weaker and moves closer to the surface. At the critical angle it runs along the surface. Above the critical angle, all the light reflects.
• Everyday examples of total internal reflection:
  • Prisms in periscopes and binoculars reflect light through 90° or 180°.
  • A swimmer or diver under water looks up and sees the water surface shining like a mirror.
  • Optical fibres carry light along thin glass threads, for example in decorative lamps and in endoscopes (used by doctors to see inside the body).
• Refractive index, n, is the ratio of the speeds of light in two different regions. For light going from region 1 into region 2, n = speed in region 1 ÷ speed in region 2. It has no unit. Extended
• Usually region 1 is a vacuum. Then n = speed of light in a vacuum ÷ speed of light in the material. This is the refractive index of the material. Extended
• The speed of light in air is almost the same as in a vacuum. So you can also use the speed in air. Extended
• A larger n means light is slower in the material and is bent more. Extended
• For light going from air into a material: n = sin i / sin r. Here i is the angle in air and r is the angle in the material. Extended
• The critical angle and the refractive index are linked by n = 1 / sin c. A larger n gives a smaller critical angle. Extended
• Optical fibres are thin, flexible threads of very clear glass. Light (or infrared) enters one end. It hits the side of the fibre at an angle of incidence greater than the critical angle. So it is totally internally reflected, again and again, all the way along the fibre. Very little light is lost, even when the fibre bends gently. Extended
• In telecommunications, optical fibres carry telephone calls, internet data and cable television as very fast pulses of light or infrared. They can carry a lot of data each second over long distances. Undersea optical fibre cables link the Maldives to other countries. Extended

3.2.3 Thin lenses

• A converging lens is thicker in the middle than at the edges. It bends a parallel beam of light inwards, so the rays meet at one point.
• A diverging lens is thinner in the middle than at the edges. It bends a parallel beam of light outwards, so the rays spread apart.
• The principal axis is the line through the centre of the lens at right angles to the lens.
• The principal focus (focal point), F:
  • for a converging lens: the point on the principal axis where rays parallel to the axis meet after passing through the lens.
  • for a diverging lens: the point on the principal axis from which rays parallel to the axis seem to come after passing through the lens. It is on the same side as the light coming in.
• The focal length, f, is the distance along the principal axis from the centre of the lens to the principal focus. Unit: m or cm.
• A lens has a principal focus on each side, both at the same distance from the centre.
• To show the action of a diverging lens on a parallel beam in a diagram: draw the rays spreading out after the lens. Then extend them backwards with dashed lines. The dashed lines meet at F on the side the light came from.
• Real image: the rays of light really meet there. A real image can be shown on a screen.
• A virtual image is formed where diverging rays seem to come from. You find it by extending the rays backwards (dashed lines). The rays never really meet there, so a virtual image cannot be shown on a screen.
• Describe any image with three words, one from each pair:
  • enlarged, same size or diminished (smaller than the object)
  • upright or inverted (upside down)
  • real or virtual.
• Ray diagram for a real image (converging lens):
  1. Draw the principal axis as a horizontal line. Draw the lens as a vertical line across it.
  2. Mark F on both sides of the lens, one focal length from the centre. Mark 2F at twice the focal length on both sides.
  3. Draw the object as an upright arrow standing on the axis, further from the lens than F.
  4. Ray 1: from the top of the object, draw a ray parallel to the principal axis as far as the lens. After the lens, draw it passing through F on the other side.
  5. Ray 2: from the top of the object, draw a ray through the centre of the lens. It goes straight on and does not bend.
  6. (Check ray, if you want one.) Ray 3: from the top of the object, draw a ray through F on the object side to the lens. After the lens, it travels parallel to the axis.
  7. The point where the rays cross is the top of the image. Draw the image as an arrow from the axis to this point.
  8. Treat each ray as bending once, at the centre line of the lens. Use a ruler and put arrows on every ray.
• Results with a converging lens (object further away than F; the image is on the other side of the lens):
  • object beyond 2F: image real, inverted, diminished, between F and 2F.
  • object at 2F: image real, inverted, same size, at 2F.
  • object between F and 2F: image real, inverted, enlarged, beyond 2F.
• Extra detail: if the object is exactly at F, the rays leave the lens parallel. They never meet, so no image is formed.
• Ray diagram for a virtual image (converging lens): this happens when the object is between F and the lens. Extended
  1. Draw the axis, the lens and F on both sides, as before. Draw the object closer to the lens than F.
  2. Draw Ray 1: parallel to the axis to the lens, then through F on the other side.
  3. Draw Ray 2: through the centre of the lens, straight on.
  4. After the lens the two rays spread apart. They do not meet.
  5. Extend both rays backwards with dashed lines, on the object side of the lens.
  6. The point where the dashed lines meet is the top of the image. Draw the image as a dashed arrow.
  7. The image is virtual, upright and enlarged. It is on the same side of the lens as the object, and further from the lens.
• Magnifying glass: a single converging lens held so that the object is closer to the lens than F (inside the focal length). You look through the lens from the other side. You see an upright, enlarged, virtual image. Extended
• In the eye, the lens forms a real image on the retina at the back of the eye. To see clearly, the image must be exactly on the retina. Extended
• Short sight: a person sees near objects clearly but distant objects look blurred. Light from a distant object is brought to a focus in front of the retina. Extended
• Short sight is corrected with a diverging lens. The lens spreads the rays out a little before they enter the eye. Then the eye brings them to a focus on the retina. Extended
• Long sight: a person sees distant objects clearly but near objects look blurred. Light from a near object would be brought to a focus behind the retina. Extended
• Long sight is corrected with a converging lens. The lens bends the rays inwards a little before they enter the eye. Then the eye brings them to a focus on the retina. Extended

3.2.4 Dispersion of light

• White light is a mixture of many colours.
• Dispersion is the splitting of white light into its colours.
• A glass prism shows dispersion. White light refracts as it enters the prism and again as it leaves. Glass slows each colour by a slightly different amount, so each colour bends by a different amount. The colours spread out into a spectrum.
• Violet light is bent the most. Red light is bent the least.
• The traditional seven colours of the visible spectrum are: red, orange, yellow, green, blue, indigo, violet.
• In order of increasing frequency: red → orange → yellow → green → blue → indigo → violet.
• In order of increasing wavelength: violet → indigo → blue → green → yellow → orange → red.
• Red has the longest wavelength and the lowest frequency. Violet has the shortest wavelength and the highest frequency.
• Monochromatic light is visible light of a single frequency. So it is a single colour. Extended
• Example: light from a laser is very close to monochromatic. A monochromatic ray is not split up by a prism, because there is only one frequency. Extended

Common mistakes

• Students measure the angle of incidence from the mirror or the surface of the block. / The mark scheme wants: angles measured from the normal.
• Students write that a plane mirror image is on the surface of the mirror. / The mark scheme wants: the image is the same distance behind the mirror as the object is in front.
• Students write that light bends towards the normal when it enters air from glass. / The mark scheme wants: light speeds up and bends away from the normal when it goes from glass into air.
• Students write that total internal reflection happens when light goes from air into glass. / The mark scheme wants: light travelling from glass (or water) towards air, with the angle of incidence greater than the critical angle.
• Students write that a virtual image can be seen on a screen. / The mark scheme wants: a virtual image is where diverging rays seem to come from; it cannot be formed on a screen.
• Students write that a prism adds colours to white light. / The mark scheme wants: white light is already a mixture of colours; the prism separates them because each colour refracts by a different amount.
• Students use the angle inside the glass as i in n = sin i / sin r. / The mark scheme wants: i is the angle in air, r is the angle in the material. Extended
• Students write that short sight is corrected with a converging lens. / The mark scheme wants: short sight → diverging lens; long sight → converging lens. Extended

Exam tips

• Define the normal as a line at right angles to the surface, at the point where the ray meets it. Define each angle (incidence, reflection, refraction) as the angle between the ray and the normal.
• Draw ray diagrams with a sharp pencil and a ruler. Put an arrow on every ray. Use dashed lines for normals and for virtual rays.
• Describe an image with all three words: for example “real, inverted, diminished”. Each word is often a separate mark.
• State the two conditions for total internal reflection. Many answers lose a mark by giving only one.
• Describe the refraction experiment as numbered steps: what you draw, what you mark, what you measure, and what you repeat.
• Calculate with sin: set your calculator to degrees. Write the equation first, then the substitution, then the answer. Refractive index has no unit. Extended
• Explain how an optical fibre works in three steps: light hits the side at more than the critical angle; it is totally internally reflected; this repeats all along the fibre. Extended
• A typical 1-mark answer: “The critical angle is the angle of incidence for which the angle of refraction is 90°.”
• A typical 2-mark answer to “Describe the image in a plane mirror”: “It is virtual and the same size as the object (1). It is as far behind the mirror as the object is in front (1).”
• A typical 3-mark answer to “How does a magnifying glass work?”: “It is a converging lens (1). The object is placed closer to the lens than the principal focus (1). The image is virtual, upright and enlarged (1).” Extended