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Critical angle and total internal reflection
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When light tries to leave glass at a steep enough angle, it is all reflected back inside. This is how optical fibres work.
Critical angle
Light travelling from glass into air bends away from the normal.
The critical angle c is the angle of incidence (inside the glass) for which the angle of refraction is 90°.
If the angle of incidence is bigger than c, all the light is reflected back: total internal reflection (TIR).
The critical angle c is the angle of incidence (inside the glass) for which the angle of refraction is 90°.
If the angle of incidence is bigger than c, all the light is reflected back: total internal reflection (TIR).
Calculating it
sin c = 1 ÷ n
For glass with n = 1.5: sin c = 0.667, so c ≈ 42°.
TIR needs two conditions: light going from a denser material (higher n) towards a less dense one, and an angle of incidence greater than c.
For glass with n = 1.5: sin c = 0.667, so c ≈ 42°.
TIR needs two conditions: light going from a denser material (higher n) towards a less dense one, and an angle of incidence greater than c.
Uses
Optical fibres: light travels along a thin glass fibre by repeated total internal reflection. Used for communications (internet, telephone) and in endoscopes to see inside the body.
Prisms: a 45° glass prism reflects light through 90° or 180° by TIR, because 45° is greater than the critical angle of glass. Used in periscopes and binoculars.
Prisms: a 45° glass prism reflects light through 90° or 180° by TIR, because 45° is greater than the critical angle of glass. Used in periscopes and binoculars.
Calculate the critical angle for water, n = 1.33.
- sin c = 1 ÷ 1.33 = 0.752
- c = sin-1(0.752)
Answer: c ≈ 48.8°
The critical angle is the angle of incidence that gives a refraction angle of 90°. Above it, total internal reflection happens. sin c = 1 ÷ n. Optical fibres and prisms use TIR.
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