Spectrometer, speed of light and optical fibres

Physics · Optical instruments. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

A spectrometer is used to study spectra and to measure angles of deviation, and so the wavelength of light. It has three parts: a collimator, a turntable and a telescope. Michelson measured the speed of light with a rotating eight-sided mirror. Light went from one face to a distant mirror and back, and a steady image was seen only when the mirror turned one-eighth of a revolution in that time.

When light in a denser medium meets a rarer medium at an angle greater than the critical angle, all of it is reflected back. This is total internal reflection. An optical fibre has a glass core surrounded by a cladding of lower refractive index, so light is trapped in the core and carries signals over long distances.

Rules to remember

Common mistake

Giving the cladding the higher refractive index, or writing sin θc as denser ÷ rarer (which is more than 1 and impossible). The core must be the denser medium.

Worked example

The core of an optical fibre has refractive index 1.50 and the cladding 1.47. Find the critical angle at the core-cladding boundary.

  1. sin θc = n2/n1 = 1.47 ÷ 1.50 = 0.98.
  2. θc = sin−1(0.98) = 78.5°.
  3. Light meeting the boundary at more than 78.5° to the normal is totally internally reflected.

Answer: θc = 78.5°.

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