Cambridge IGCSE0972

Light

Physics 0972 Chapter Notes

What this chapter covers

Light - Reflection of lightLight - Refraction of lightLight - Thin lensesLight - Dispersion of light
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1. Fundamental Properties of Light

For you to see anything, light must travel from an object to your eye. Objects that produce their own light, like the Sun or a light bulb, are called luminous. Most objects, like a book or the Moon, are non-luminous; we see them by the light they reflect from a luminous source. Light is a form of energy that travels in straight lines, which we represent using straight lines with arrows called rays. It is a transverse wave and, uniquely, can travel through a vacuum (empty space). In a vacuum, light travels at the fastest possible speed in the universe: 300,000,000 metres per second (3 x 10^8 m/s).

speed = distance / time

Key term

Luminous: An object that is a source of light, producing and emitting its own light.

Examiner insight

Examiners expect you to know that the speed of light is constant in a vacuum but it slows down when it enters different materials like water or glass.

Fun fact

If you could travel at the speed of light, you could circle the Earth's equator about 7.5 times in just one second.

Worked example 13 marks

The Sun is approximately 150,000,000 km from Earth. The speed of light is 300,000 km/s. Calculate the time it takes for light from the Sun to reach Earth.

  1. 1

    Step 1: Identify the known values. Distance = 150,000,000 km, Speed = 300,000 km/s.

  2. 2

    Step 2: State the formula: time = distance / speed.

  3. 3

    Step 3: Substitute the values into the formula: time = 150,000,000 km / 300,000 km/s.

  4. 4

    Step 4: Calculate the result: time = 500 s.

Recap

  • Luminous objects produce their own light; non-luminous objects reflect light.
  • Light travels in straight lines, represented by rays.
  • Light is a transverse wave that transfers energy and can travel through a vacuum.
  • The speed of light in a vacuum is the universal speed limit, approximately 3 x 10^8 m/s.

Quick check

  1. Give one example of a luminous object and one example of a non-luminous object.2 marks
  2. What is the approximate speed of light in a vacuum?1 mark

2. Reflection from Plane Mirrors

Reflection is when light bounces off a surface. A smooth, shiny surface like a plane (flat) mirror reflects light in a predictable way. To describe this, we imagine a line drawn at 90 degrees to the mirror's surface at the point where the light hits; this line is called the normal. The incoming ray is the incident ray, and the outgoing ray is the reflected ray. The Law of Reflection states that the angle of incidence (the angle between the incident ray and the normal) is equal to the angle of reflection (the angle between the reflected ray and the normal). The image you see in a plane mirror is virtual (it cannot be projected onto a screen), upright, laterally inverted (left and right are swapped), the same size as the object, and appears to be as far behind the mirror as the object is in front of it.

Angle of incidence (i) = Angle of reflection (r)

Key term

Virtual Image: An image formed where light rays appear to diverge from, which cannot be projected onto a screen.

Examiner insight

Accurate ray diagrams with arrows on all rays are essential for full marks in questions involving reflection. Use a ruler and protractor.

Common pitfall

A common mistake is measuring the angle of incidence from the mirror surface itself, instead of from the normal.

Worked example 13 marks

A ray of light strikes a plane mirror. The angle between the incident ray and the mirror is 30°.a) What is the angle of incidence?b) What is the angle of reflection?

  1. 1

    Step 1: Understand that the normal is at 90° to the mirror surface.

  2. 2

    Step 2 (a): The angle of incidence is the angle between the incident ray and the normal. So, angle of incidence(i) = 90° - 30° = 60°.

  3. 3

    Step 3 (b): According to the Law of Reflection, the angle of reflection(r) is equal to the angle of incidence (i).

  4. 4

    Step 4: Therefore, the angle of reflection(r) = 60°.

Recap

  • Reflection is the bouncing of light off a surface.
  • The Law of Reflection states that the angle of incidence equals the angle of reflection.
  • Angles of incidence and reflection are always measured from the normal.
  • An image in a plane mirror is virtual, upright, laterally inverted, and the same size as the object.

Quick check

  1. State the Law of Reflection.1 mark
  2. Is the image seen in a bathroom mirror real or virtual?1 mark

3. Refraction of Light

Refraction is the bending of light as it passes from one medium to another, for example, from air into glass. This happens because light travels at different speeds in different materials. A material that slows light down more is called optically denser. When light enters an optically denser medium at an angle, it bends towards the normal. When it enters a less dense medium, it bends away from the normal. The amount of bending is described by the material's refractive index (n). A higher refractive index means more bending. Snell's Law relates the angle of incidence(i) and the angle of refraction(r) with the refractive indices of the two materials.

n = sin(i) / sin(r)

n = speed of light in vacuum / speed of light in medium

Key term

Refractive Index (n): A dimensionless number that describes how much a material slows down light and causes it to bend.

Examiner insight

When drawing refraction diagrams, show the ray bending at the boundary between the two media and ensure the direction of bending (towards or away from the normal) is correct.

Common pitfall

Forgetting that light bends away from the normal when going from a denser to a less dense medium, and applying Snell's Law incorrectly in this scenario.

Worked example 13 marks

A ray of light enters a glass block from air at an angle of incidence of 45°. The angle of refraction in the glass is 28°. Calculate the refractive index of the glass.

  1. 1

    Step 1: Identify the given angles. Angle of incidence(i) = 45°, Angle of refraction(r) = 28°.

  2. 2

    Step 2: State Snell's Law for light entering from air: n = sin(i) / sin(r).

  3. 3

    Step 3: Substitute the values: n = sin(45°) / sin(28°).

  4. 4

    Step 4: Calculate the values of sin: n = 0.707 / 0.470.

  5. 5

    Step 5: Calculate the final answer: n = 1.50 (to 3 significant figures).

Recap

  • Refraction is the bending of light when it changes medium, due to a change in speed.
  • Light bends towards the normal when entering a denser medium.
  • Light bends away from the normal when entering a less dense medium.
  • Refractive index is a measure of a material's optical density.
  • Snell's Law (n = sin i / sin r) quantifies the amount of bending.

Quick check

  1. What is the primary cause of refraction?1 mark
  2. In which direction does light bend when it travels from water into air?1 mark

4. Total Internal Reflection

When light travels from a denser medium to a less dense medium (e.g., from glass to air), it bends away from the normal. As the angle of incidence increases, the angle of refraction also increases. At a specific angle of incidence, called the critical angle (c), the angle of refraction becomes 90°. If the angle of incidence is increased beyond the critical angle, the light does not exit the medium at all. Instead, it is completely reflected back into the denser medium. This phenomenon is called Total Internal Reflection (TIR). For TIR to occur, two conditions must be met: 1. Light must be travelling from a more optically dense medium to a less optically dense one. 2. The angle of incidence must be greater than the critical angle.

sin(c) = 1 / n

n₁ sin(θ₁) = n₂ sin(θ₂)

Key term

Critical Angle (c): The angle of incidence in a denser medium for which the angle of refraction in the less dense medium is 90°.

Fun fact

The sparkle of a well-cut diamond is due to its very high refractive index and thus very small critical angle (about 24°), causing most light entering it to be totally internally reflected multiple times before it exits.

Worked example 13 marks

The refractive index of a type of glass is 1.52. Calculate the critical angle for this glass when it is in contact with air (n≈1).

  1. 1

    Step 1: State the formula relating the critical angle and refractive index: sin(c) = 1 / n.

  2. 2

    Step 2: Substitute the given refractive index: sin(c) = 1 / 1.52.

  3. 3

    Step 3: Calculate the value of the fraction: sin(c) = 0.6579.

  4. 4

    Step 4: Find the angle by taking the inverse sine: c = sin⁻¹(0.6579).

  5. 5

    Step 5: Calculate the final answer: c = 41.1°.

Worked example 24 marks

Explain how optical fibres use total internal reflection to transmit information.

  1. 1

    Step 1: Describe the structure. An optical fibre consists of a very thin, flexible core made of glass or plastic, surrounded by cladding of a lower refractive index.

  2. 2

    Step 2: Explain the process. Light signals (pulses) are sent into one end of the core at an angle greater than the critical angle.

  3. 3

    Step 3: Link to TIR. As the light travels along the fibre, it continuously strikes the core-cladding boundary at an angle greater than the critical angle, causing it to undergo total internal reflection repeatedly.

  4. 4

    Step 4: Conclude. This traps the light within the core, allowing it to travel long distances with very little energy loss or signal degradation.

Recap

  • Total Internal Reflection (TIR) occurs when light is completely reflected at a boundary.
  • Condition 1 for TIR: Light must travel from a denser to a less dense medium.
  • Condition 2 for TIR: The angle of incidence must be greater than the critical angle.
  • The critical angle 'c' is related to the refractive index 'n' by sin(c) = 1/n.
  • Optical fibres and periscopes are key applications of TIR.

Quick check

  1. State the two conditions required for total internal reflection.2 marks
  2. What happens if light hits the boundary at an angle exactly equal to the critical angle?1 mark

5. Image Formation by a Converging Lens

A lens is a piece of transparent material shaped to refract light in a specific way. A convex or converging lens is thicker in the middle than at the edges. It causes parallel rays of light to converge and meet at a single point called the principal focus or focal point (F). The distance from the centre of the lens to the principal focus is the focal length (f). The type of image formed by a converging lens depends on the object's distance from the lens. If the object is placed further away than the focal length, the lens produces a real, inverted image. This is how cameras and projectors work. If the object is placed closer than the focal length, the lens produces a virtual, upright, and magnified image. This is how a magnifying glass works.

Key term

Principal Focus (Focal Point): The point where rays of light parallel to the principal axis converge after passing through a converging lens.

Examiner insight

Marks are awarded for drawing at least two correct construction rays from the top of the object to locate the image, with the final image clearly drawn and described.

Common pitfall

Forgetting to draw arrows on the rays to show the direction of light travel, which is essential for marks on ray diagrams.

Worked example 14 marks

An object is placed at a distance of 2F from a converging lens, where F is the principal focus. By drawing a ray diagram, find the position and nature of the image formed.

  1. 1

    Step 1: Draw the principal axis, the lens, and mark the positions F and 2F on both sides of the lens.

  2. 2

    Step 2: Draw the object as an upright arrow at position 2F.

  3. 3

    Step 3: Draw Ray 1: A ray from the top of the object, parallel to the principal axis. After passing through the lens, this ray refracts through the principal focus (F) on the other side.

  4. 4

    Step 4: Draw Ray 2: A ray from the top of the object that passes through the optical centre of the lens. This ray continues undeviated.

  5. 5

    Step 5: The image is formed where the two refracted rays intersect. Mark this point and draw the image as an arrow from the axis to this point.

  6. 6

    Step 6: Describe the image. The image is formed at 2F on the other side of the lens. It is real (formed by actual intersection of rays), inverted (upside down), and the same size as the object.

Recap

  • A converging (convex) lens is thicker in the middle and brings parallel rays to a focus.
  • The focal length is the distance from the lens centre to the principal focus.
  • An object placed beyond F forms a real, inverted image.
  • An object placed within F forms a virtual, upright, magnified image.
  • Ray diagrams use at least two standard rays to locate the image.

Quick check

  1. What is another name for a converging lens?1 mark
  2. To use a converging lens as a magnifying glass, where must the object be placed?1 mark

6. The Electromagnetic Spectrum

Visible light is just one small part of a much larger family of waves called the electromagnetic (EM) spectrum. All EM waves are transverse waves, can travel through a vacuum, and travel at the same speed in a vacuum (the speed of light, 3 x 10^8 m/s). They differ only in their wavelength and frequency. The spectrum, in order of increasing wavelength (and decreasing frequency/energy), is: Gamma rays, X-rays, Ultraviolet, Visible light, Infrared, Microwaves, Radio waves. Each part of the spectrum has different properties and uses. For example, radio waves are used for broadcasting, microwaves for cooking and communication, infrared for remote controls and thermal imaging, and X-rays for medical imaging.

wave speed (c) = frequency (f) × wavelength (λ)

Key term

Electromagnetic Spectrum: The continuous range of electromagnetic waves, from high-frequency gamma rays to low-frequency radio waves.

Examiner insight

You must know the correct order of the seven main types of electromagnetic waves. A mnemonic like 'Raging Martians Invaded Venus Using X-ray Guns' can be helpful.

Fun fact

Your Wi-Fi, your microwave oven, the light you see with, and the X-ray at the hospital are all fundamentally the same thing (EM waves), just with different wavelengths.

Worked example 13 marks

A radio station broadcasts at a frequency of 102 MHz. Calculate the wavelength of these radio waves. (Speed of EM waves = 3.0 x 10^8 m/s)

  1. 1

    Step 1: Convert the frequency to Hz. 102 MHz = 102 x 10^6 Hz.

  2. 2

    Step 2: State the wave equation: speed = frequency × wavelength (c = fλ).

  3. 3

    Step 3: Rearrange the formula to find wavelength: wavelength (λ) = speed(c) / frequency (f).

  4. 4

    Step 4: Substitute the values: λ = (3.0 x 10^8 m/s) / (102 x 10^6 Hz).

  5. 5

    Step 5: Calculate the result: λ = 2.94 m.

Recap

  • The EM spectrum is a continuous family of waves that all travel at the speed of light in a vacuum.
  • The order is: Radio, Microwaves, Infrared, Visible, UV, X-rays, Gamma rays (by increasing frequency).
  • Visible light is a small part of the EM spectrum, with colours from Red (long λ) to Violet (short λ).
  • All EM waves obey the wave equation: c = fλ.

Quick check

  1. Which type of EM wave has the highest frequency?1 mark
  2. List the colours of the visible spectrum in order of increasing wavelength.1 mark

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. The star Proxima Centauri is 4.2 light-years away from Earth. A light-year is the distance light travels in one year. Calculate this distance in kilometres. (1 year = 3.15 x 10^7 s, speed of light = 3.0 x 10^8 m/s).4 marks
  2. A student stands 2.5 m in front of a large plane mirror. How far behind the mirror does her image appear to be? List three other characteristics of the image.4 marks
  3. Light travels from air into a diamond. The angle of incidence is 30° and the angle of refraction is 12°. Calculate the refractive index of the diamond.3 marks
  4. The refractive index of water is 1.33. Calculate the critical angle for the water-air boundary.3 marks
  5. Draw a ray diagram to show how a converging lens can be used as a magnifying glass. Label the object, image, and principal focus. State the nature of the image formed.4 marks
  6. a) List the seven main regions of the electromagnetic spectrum in order of increasing frequency. b) For both microwaves and ultraviolet waves, state one practical application and one potential danger.6 marks
  7. Explain, with the aid of a diagram, the two conditions necessary for total internal reflection to occur at a glass-air boundary.4 marks
  8. A ray of light is incident on a plane mirror at an angle of 25° to the mirror surface. The mirror is then rotated by 10° so the angle to the incident ray is now 15°. What is the angle between the original reflected ray and the new reflected ray?5 marks
  9. An object of height 2 cm is placed 30 cm in front of a converging lens of focal length 10 cm. By drawing an accurate scale diagram, determine the position, height, and nature of the image.5 marks
  10. Visible light is composed of a spectrum of colours. a) Which colour has the longest wavelength? b) Explain what is meant by the term 'monochromatic light'. c) A green laser has a wavelength of 532 nm. Calculate its frequency. (1 nm = 10⁻⁹ m).4 marks

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