Cambridge O Level Physics · Syllabus 5054 · Waves
Refractive Index
What is Refractive Index?
Refractive index n is defined as the ratio of the sine of the angle of incidence to the sine of the angle of refraction for light passing from air into the medium; it has no unit and is greater than one for transparent solids and liquids.
This definition is part of the Waves chapter in Cambridge O Level Physics.
Refractive Index in context
Light changes speed when it crosses from one transparent medium into another, and if it meets the boundary at an angle to the normal it also changes direction. Entering a medium in which light travels more slowly, the ray bends towards the normal; entering one in which it travels faster, it bends away from the normal. A ray along the normal changes speed but not direction. The refractive index \(n = \dfrac{\sin i}{\sin r}\) measures how strongly a medium refracts light, and the critical angle \(c\), given by \(n = \dfrac{1}{\sin c}\), is the angle of incidence in the denser medium that produces a refracted ray along the boundary.
White light is a mixture of all the visible frequencies. A glass prism separates them because the refractive index of glass is slightly different for each frequency: violet is refracted (and so deviated) most, red least. The colours therefore emerge along slightly different directions and spread out into a spectrum. The prism does not create the colours — it separates colours that were in the white light all along.
Common mistakes with Refractive Index
- 11. “The critical angle works in either travel direction.” Why wrongLight entering a denser medium bends towards the normal, so the angle inside can never reach 90°; there is nothing for a critical angle to mark. CorrectThe critical angle is defined for light travelling from higher refractive index to lower. Say this“The critical angle is the angle of incidence in the denser medium for which the angle of refraction is 90°.” CheckDoes a ray going from air into glass have a critical angle? (No.)
- 15. “A prism creates the colours.” Why wrongIsolate one colour and send it through a second prism: it stays that colour. Nothing new is manufactured. CorrectWhite light is already a mixture of frequencies; the prism separates them because glass refracts each frequency by a slightly different amount. Say this“The prism separates the colours already present in white light, because the refractive index of glass is slightly different for each frequency.” CheckWhat is seen if a second, inverted prism is placed after the first?
Examiner tips on Refractive Index
- Three habits that raise a mark without adding knowledge. (1) Answer the command word you were given, not the one you wish you had. If it says “explain”, every sentence needs a reason. (2) Put the unit on every numerical answer and none on a ratio — refractive index and magnification have no units. (3) Give the number of significant figures the data justify: two-figure data cannot support a four-figure answer.