Edexcel IGCSE Physics · Spec 3.18-3.20
Refractive Index & Total Internal Reflection
Refractive index and total internal reflection.
Physics revision video
Refractive Index & Total Internal Reflection
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Explained
Refractive index, the critical angle, and getting light trapped
Light changes speed when it enters a new material, and that change of speed is what bends it. Refractive index is a single number describing how strongly a material does that. The larger the refractive index, the more the light slows and the more it bends.
For light going from air into a material, n equals sine i divided by sine r, where i is the angle of incidence and r is the angle of refraction. Refractive index has no unit, because it is one number divided by another.
Which way it bends
Going from air into glass, the light slows down and bends towards the normal, so r is smaller than i. Going from glass out into air, it speeds up and bends away from the normal, so the refracted angle is larger.
Because n is always greater than one for real materials, a calculated value below one is a signal that you have divided the wrong way round. Check before you write it down.
Total internal reflection
Increase the angle inside the glass and the emerging ray bends further and further from the normal. At one particular angle it would emerge along the surface itself. That angle is the critical angle.
Beyond it, no light escapes at all. It is all reflected back inside, which is total internal reflection. Two conditions must both hold, and a complete answer states both: the light must be travelling from a material of higher refractive index into one of lower refractive index, and the angle of incidence must be greater than the critical angle.
The link to refractive index is sine of the critical angle equals one divided by n. A higher refractive index gives a smaller critical angle, so light is trapped more easily inside a denser material.
What examiners say about this topic
Principal examiner reports for Edexcel International GCSE Physics identify the same weaknesses across two series. Candidates found describing total internal reflection surprisingly challenging; they often scored for one of the required conditions, but attempts at describing the effect itself were usually too imprecise to be given credit. A later report says few learners clearly linked refractive index, critical angle and total internal reflection, and that explanations were often vague or incomplete.
Angle measurement is the other recurring loss. One report notes errors in measuring angles from the normal, with many candidates measuring the wrong angle, and that although most knew the ray would emerge into the air, only a quarter drew it refracting in the correct direction. Another records learners giving values such as 40, 90 or 130 degrees for an angle, and frequent misuse of the formula producing refractive indices less than one.
The fix is mechanical. Draw the normal first, as a dashed line at right angles to the surface where the ray meets it, and take every angle between the ray and that line rather than between the ray and the surface.
Where it is used
Optical fibres carry light along a glass core by total internal reflection. The light strikes the boundary at more than the critical angle every time, so none escapes, and the signal follows the fibre round bends. This carries telephone and internet data, and in an endoscope it carries an image out of the body.
Prisms in binoculars and periscopes use the same effect at 45 degrees, because glass has a critical angle of about 42 degrees. A prism reflects more completely than a mirror, which loses a little light at its silvered backing.
Spec 3.18-3.20
What you need to know
- Understand refractive index n
- Explain total internal reflection
- Describe the critical angle and its uses
Active recall
Quick check
Answer each question before opening the answer.
What is the critical angle?
The angle of incidence in the denser medium above which total internal reflection occurs.
What two conditions are needed for total internal reflection?
Light must travel from a denser to a less dense medium, and the angle of incidence must exceed the critical angle.
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