OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(e) critical angle; sin C = 1/n; total internal reflection for light.
Full specification wording
Electromagnetic waves: (e) critical angle; sin C = 1/n; total internal reflection for light.
When light travels from a denser medium of refractive index n towards a less dense medium such as air, the angle of refraction is larger than the angle of incidence.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 6 of 6
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
When light travels from a denser medium of refractive index n towards a less dense medium such as air, the angle of refraction is larger than the angle of incidence. At the critical angle C, the refracted ray emerges along the boundary at 90° to the normal, so n sin C = 1 × sin 90° = 1, giving sin C = 1/n. For angles of incidence greater than C, no light refracts out; it is all reflected back inside the medium, which is total internal reflection. Example: for glass with n = 1.50, sin C = 1/1.50 = 0.667, so C = 41.8°. Total internal reflection requires the light to be travelling towards a less optically dense medium and i > C.
What earns the marks
- The critical angle C is the angle of incidence in the denser medium for which the angle of refraction is 90°.
- At the critical angle, n sin C = 1, so sin C = 1/n where n is the refractive index of the denser medium relative to the less dense medium.
- Total internal reflection occurs when light travels towards a less optically dense medium and the angle of incidence exceeds C.
- At i > C no light is refracted out of the medium; all the light is reflected internally.
- Example: for n = 1.50, sin C = 1/1.50 = 0.667, so C = 41.8°.
- Total internal reflection cannot occur when light travels from a less dense to a denser medium.
Common mistakes and how to put them right
Using sin C = n instead of sin C = 1/n.
Put it right: C is found from the reciprocal of n.
Thinking total internal reflection can happen at any boundary.
Put it right: Light must be going from a denser to a less dense medium.
Confusing the critical angle with the angle of refraction.
Put it right: C is the angle of incidence in the denser medium when the refracted angle is 90°.
Believing some light still refracts out at i > C.
Put it right: Beyond C all the light is internally reflected.
Exam tips
- Check that n > 1 before using sin C = 1/n; if n < 1 you have inverted the ratio.
- State both conditions for total internal reflection: denser-to-less-dense direction and i > C.
- Give C to a sensible number of significant figures, for example 41.8° for n = 1.50.
Try the lesson
The start of the Electromagnetic waves: (e) critical angle; sin C = 1/n; total internal reflection for light. lesson, made from checked teaching notes for this specification point.
Listen
When light travels from a denser medium of refractive index n towards a less dense medium such as air, the angle of refraction is larger than the angle of incidence. At the critical angle C, the refracted ray emerges along the boundary at 90° to the normal, so n sin C = 1 × sin 90° = 1, giving sin C = 1/n. For angles of incidence greater than C, no light refracts out; it is all reflected back inside the medium, which is total internal reflection. Example: for glass with n = 1.50, sin C = 1/1.50 = 0.667, so C = 41.8°. Total internal reflection requires the light to be travelling towards a less optically dense medium and i > C. A strong answer earns marks for these points. The critical angle C is the angle of incidence in the denser medium for which the angle of refraction is 90°. At the critical angle, n sin C = 1, so sin C = 1/n where n is the refractive index of the denser medium relative to the less dense medium. Total internal reflection occurs when light travels towards a less optically dense medium and the angle of incidence exceeds C. At i > C no light is refracted out of the medium; all the light is reflected internally. A common slip: Using sin C = n instead of sin C = 1/n. Instead, C is found from the reciprocal of n. Exam tip: Check that n > 1 before using sin C = 1/n; if n < 1 you have inverted the ratio.
Key words
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Critical angle
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sin C = 1/n
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Total internal reflection
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See every definition
- Critical angle
- The angle of incidence in the denser medium for which the angle of refraction is 90°, so the refracted ray emerges along the boundary.
- sin C = 1/n
- At the critical angle, n sin C = 1 × sin 90° = 1, giving sin C = 1/n where n is the refractive index of the denser medium relative to the less dense medium.
- Total internal reflection
- Occurs when light travels towards a less optically dense medium and the angle of incidence exceeds C, so no light refracts out and all the light is reflected internally.
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