Ch 3 · 3.2.2 Refraction of Light · O Level Physics 5054
Topic 3 of 7 in Waves — O Level Physics 5054 — 47 lessons.
Introduction
A straw in a glass of water looks bent at the surface. A swimming pool looks shallower than it really is. Both happen because light changes speed, and so changes direction, when it passes from one material into another. This is refraction. The same physics lets optical fibres carry internet signals under the oceans. (Syllabus section 3.2.2.)
Key ideas — Refraction and the words you need
When light crosses the boundary between two transparent materials at an angle, it changes direction, because its speed changes.
🧑🏫 Teacher's explanation
Imagine you are running from a paved sidewalk into a deep, thick sandpit at an angle. As your lead foot hits the sand, it slows down instantly. Because the side of your body hitting the sand first is moving slower than the side still on the pavement, your path is forced to pivot. This is exactly what light does when it moves between materials of different densities.
📖 Definitions
🔍 Worked example — Standard
Light travels from glass (n = 1.52) into air. Calculate the critical angle c.
🔍 Worked example — Exam-style
A laser beam is sent into an optical fiber. The core has a refractive index of 1.48 and the cladding has a refractive index of 1.45. Calculate the minimum angle of incidence (relative to the normal) required for total internal reflection to occur within the core.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Key ideas — Refractive index
The refractive index n of a material measures how much it bends light entering it from air (or a vacuum):
🧑🏫 Teacher's explanation
Imagine you are running from a paved sidewalk into a deep pool of water. As soon as your feet hit the water, you slow down. If you were running at an angle, that sudden change in speed causes your path to bend. Light does the exact same thing; it changes direction because it changes speed when moving from one medium to another.
📖 Definitions
🔍 Worked example — Easy
A ray of light travels from air into a glass block. The angle of incidence is 35^° and the angle of refraction is 21^°. Calculate the refractive index n of the glass.
🔍 Worked example — Standard
Light travels from glass (n = 1.52) into air. Calculate the critical angle c for this glass-air boundary.
🔍 Worked example — Exam-style
A fiber optic cable has a core with a refractive index of 1.45. If light enters the core from air, what is the maximum angle of incidence i it can have to undergo total internal reflection at the boundary with air? (Assume the cladding has n=1.00)
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Key ideas — Critical angle and total internal reflection
When light travels from glass (or water) towards air, it bends away from the normal. Increase the angle of incidence inside the glass:
🧑🏫 Teacher's explanation
Imagine you are swimming underwater looking up at the surface. If you look straight up, you see the sky clearly. But as you tilt your head further and further back, the surface starts to act like a mirror, reflecting the bottom of the pool back to you instead of letting light from the sky through. This happens because light changes speed when it moves between different materials.
📖 Definitions
🔍 Worked example — Easy
A ray of light travels from glass into air. The angle of incidence inside the glass is 30^° and the angle of refraction in the air is 42^°. Calculate the refractive index n of the glass.
🔍 Worked example — Standard
Calculate the critical angle c for a glass block with a refractive index of 1.52.
🔍 Worked example — Exam-style
A light ray travels from water (n = 1.33) towards the surface. Determine if total internal reflection occurs when the angle of incidence is 50^°.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Key ideas — Optical fibres
An optical fibre is a very thin, flexible strand of glass. Light enters one end and hits the inside wall at an angle greater than the critical angle, so it is totally internally reflected again and again, zig-zagging along the fibre even around bends.
🧑🏫 Teacher's explanation
Imagine you are trying to run through a corridor of mirrors. If you run straight at a mirror, you just hit it. But if you run at a very shallow angle, you bounce off the side and keep going down the hall. This is exactly how light behaves in an optical fibre. Instead of passing through the glass and escaping, the light 'bounces' off the internal walls.
📖 Definitions
🔍 Worked example — Easy
A ray of light travels from glass (n = 1.50) into air. Calculate the critical angle c.
🔍 Worked example — Standard
Light travels from water (n = 1.33) into air. Determine if a ray hitting the surface at an angle of incidence of 50^° will undergo total internal reflection.
🔍 Worked example — Exam-style
An optical fibre has a refractive index of 1.60. Calculate the critical angle for the glass-air boundary.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Practical notes
Repeat with blocks of other shapes: a triangular prism (the ray bends twice and is deviated towards the base) and a semicircular block (a ray aimed at the centre of the flat face enters the curved side along a normal and does not bend there).
Worked example
Example 1. A ray enters glass from air at an angle of incidence of 40°. The angle of refraction is 25°. Find the refractive index.
🔍 Worked example — Easy
A ray of light enters a glass block from air. The angle of incidence is 40^° and the angle of refraction is 25^°. Calculate the refractive index of the glass.
⚠️ Common errors
Common mistakes
Practice
Answers: (1) n = sin i / sin r, the ratio of the sine of the angle of incidence in air to the sine of the angle of refraction in the material. (2) n = sin 60° / sin 35° = 0.866 / 0.574 = 1.51. (3) Light travels from a denser material towards a less dense one; the angle of incidence is greater than the critical angle. (4) n = 1/sin 39° = 1/0.629 = 1.59. (5) Any two: carry much more information; less signal loss over long distances; no electrical interference; more secure; thinner and lighter.