OxfordAQA International GCSE Physics: Reflection, refraction and total internal reflection (9203) – Revision Notes

These notes condense sections 3.3.4 and 3.3.5 of the OxfordAQA International GCSE Physics (9203) specification, for exams from May/June 2018 onwards. The qualification is untiered. For full explanations and worked examples, read the study guide, then try the practice questions.

Course pages: the OxfordAQA International GCSE Physics hub, the printable checklist and the free diagnostics.

Key definitions

Term	Meaning
Normal	Construction line at 90° to the surface at the point of incidence. All angles are measured from it
Angle of incidence, i	Angle between the incident ray and the normal
Angle of reflection	Angle between the reflected ray and the normal. It equals i
Refraction	Change in wave speed at a boundary. A slanted wave also changes direction
Refractive index, n	(speed of light in vacuum (air)) / (speed of light in the medium)
Dispersion	Splitting of white light into a spectrum, for example by a prism
Critical angle, c	Angle of incidence, measured in the denser medium, at which the refracted ray just skims along the boundary
Total internal reflection	All light reflected back into the denser medium when i is greater than c

Formulas

Relationship	Notes
n = c / v	n has no unit and is greater than 1. c is the speed of light in a vacuum
n = sin i / sin r	Light going from air into the medium. Angles from the normal
n = 1 / sin c	Medium to air. c is measured in the denser medium
v = f × λ	In refraction f stays the same, so v and λ change in proportion

Rearrangements: v = c / n, sin r = sin i / n, sin c = 1 / n.

3.3.4 Reflection in brief

• Angle of incidence = angle of reflection, both from the normal.
• Plane mirror image: virtual (cannot be shown on a screen), upright, laterally inverted. Same size, and the same distance behind the mirror as the object is in front.
• Ray diagram method:
  1. Draw two rays from one point of the object to the mirror.
  2. Draw dashed normals.
  3. Reflect each ray with equal angles.
  4. Extend the reflected rays backwards with dashed lines. The image is where they cross.

3.3.5 Refraction in brief

• Enters a denser medium (slower): bends towards the normal.
• Enters a less dense medium (faster): bends away from the normal.
• Along the normal: speed changes, direction does not.
• Wavefront explanation: one end of the wavefront enters first and changes speed first, which pivots the wavefront. Slower means shorter wavelength with the same frequency.
• Prism: refracts at both faces. Each colour is bent by a different amount. Red is bent least and violet most.

Methods in steps

Find the refraction angle (air into medium)

1. Write sin r = sin i / n.
2. Work out sin i, divide by n.
3. Use inverse sine for r.
4. Check the direction: r should be smaller than i when entering a denser medium.

Find the critical angle

1. Write sin c = 1 / n.
2. Use inverse sine for c.

Decide whether TIR happens

1. Is the light inside the denser medium heading for a less dense one? If not, no TIR.
2. Compare i with c. Greater than c: total internal reflection. Less than c: it refracts out, with the angle from sin r = n sin i.

Required practical (refraction by different substances)

1. Outline a block on paper and draw a normal.
2. Send a thin ray at a chosen i and mark crosses on the paths in and out.
3. Remove the block and join the points to find the ray inside.
4. Measure i and r from the normal.
5. Repeat for at least five values of i.
6. Plot sin i against sin r. The gradient is n.

Quick worked reminders

• Glass with n = 1.60: c = sin⁻¹(1 / 1.60) = 38.7°.
• Light travels at 1.80 × 10⁸ m/s in a plastic: n = 3.00 × 10⁸ / 1.80 × 10⁸ = 1.67.
• Air into n = 1.60 at 30°: sin r = 0.5 / 1.60 = 0.3125, so r = 18.2°.

Worked reminders for the practical and dispersion

• Practical result: a plastic gave r = 16° for i = 25°. n = sin 25° / sin 16° = 0.423 / 0.276 = 1.53, and the graph gradient should agree.
• Dispersion: if violet light has n = 1.53, its speed is 3.00 × 10⁸ / 1.53 = 1.96 × 10⁸ m/s, a little slower than red (n = 1.51 gives 1.99 × 10⁸ m/s), so violet bends more.
• Wavelength in a medium: with f = 5.50 × 10¹⁴ Hz and v = 2.00 × 10⁸ m/s, λ = 2.00 × 10⁸ / 5.50 × 10¹⁴ = 3.64 × 10⁻⁷ m.
• Fibre transit time: v = 3.00 × 10⁸ / 1.48 = 2.03 × 10⁸ m/s, so 2.0 km takes 9.9 × 10⁻⁶ s.

Optical fibres

• A thin glass or plastic strand. Light or infrared hits the wall at an angle greater than c every time, so it is totally internally reflected along the fibre.
• Medicine: endoscopes show the inside of the body through a small cut or opening, so there is less damage and faster recovery.
• Communications: signals sent as pulses of light or infrared. Large capacity, low signal loss over distance, no electrical interference, thin and light.

Must-know distinctions

• Refraction and reflection. Reflection: the wave bounces back from the surface. Refraction: the wave passes into the new medium and changes speed.
• Real and virtual images. Real rays pass through a real image. A virtual image is where rays appear to come from.
• Critical angle and angle of incidence. The critical angle is a property of the boundary. The angle of incidence is the one you actually have.
• Partial and total reflection. Below the critical angle some light always reflects back. Above it, all does.
• Wave speed, frequency and wavelength. Speed and wavelength change at a boundary. Frequency does not.

Quick self-test

1. State the law of reflection.
2. A ray hits a plane mirror at 25° to the surface. What is the angle of reflection?
3. Give three words that describe the image in a plane mirror.
4. Light enters glass from air. Does it bend towards or away from the normal, and why?
5. Light has speed 1.80 × 10⁸ m/s in a material. Calculate n, taking c = 3.00 × 10⁸ m/s.
6. A ray in air hits a surface at 30°. n = 1.60. Calculate r.
7. A medium has critical angle 40.0°. Calculate n.
8. A ray inside glass of n = 1.45 hits the glass-air boundary at 40°. Does TIR occur?
9. Water has n = 1.33. Calculate the speed of light in water.
10. Which colour is bent most by a prism?
11. Why does light stay inside an optical fibre?
12. A ray in air hits a block at 45° and refracts at 27°. Calculate n.

Answers

1. The angle of incidence equals the angle of reflection.
2. Angle of incidence = 90° - 25° = 65°, so the angle of reflection is 65°.
3. Virtual, upright, laterally inverted.
4. Towards the normal. Light slows down in the denser medium.
5. n = 3.00 × 10⁸ / 1.80 × 10⁸ = 1.67.
6. sin r = sin 30° / 1.60 = 0.3125, so r = 18.2°.
7. n = 1 / sin 40.0° = 1 / 0.6428 = 1.56.
8. c = sin⁻¹(1 / 1.45) = 43.6°. The angle 40° is less than c, so no TIR. Light refracts out.
9. v = 3.00 × 10⁸ / 1.33 = 2.26 × 10⁸ m/s.
10. Violet.
11. It meets the wall at an angle above the critical angle, so it is totally internally reflected each time.
12. n = sin 45° / sin 27° = 0.7071 / 0.4540 = 1.56.

Where marks are usually lost

• Taking angles from the mirror or block edge instead of the normal.
• Writing “refracted” when the answer needs “reflected”, or the reverse.
• Saying a mirror image is “reversed” without stating that it is laterally inverted.
• Leaving out the reason for bending towards the normal: the light slows down.
• Saying TIR happens when light goes from air to glass.
• Comparing i with c without first checking that the light starts in the denser medium.
• Missing the unit, or giving too many significant figures, on a calculated speed.
• Bending a ray away from the normal when it enters glass from air.
• Forgetting that frequency stays constant when wave speed changes at a boundary.
• Plotting sin i against i instead of against sin r in the practical.
• Forgetting that n has no unit.
• Quoting a protractor-based angle to more precision than the readings allow in the required practical.

Official syllabus

OxfordAQA International GCSE Physics (9203), for exams May/June 2018 onwards, published by OxfordAQA. Sections 3.3.4 and 3.3.5.