Snell's Law (Cambridge O Level Physics)

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Refractive Index & Snell's Law

Refractive Index

  • The refractive index is a number which is related to the speed of light in the material (which is always less than the speed of light in a vacuum):
  • The refractive index is a number that is always larger than 1 and is different for different materials
    • Objects which are more optically dense have a higher refractive index, eg. n is about 2.4 for diamond
    • Objects which are less optically dense have a lower refractive index, eg. n is about 1.5 for glass

  • Since refractive index is a ratio, it has no units

Snell's Law

  • When light enters a denser medium (such as glass) it slows down and bends towards the normal
    • How much the light bends depends on the density of the material

Refraction of Light, downloadable IGCSE & GCSE Physics revision notes

Angle of incidence i and angle of refraction r through a glass block

  • If light travels from a less dense to a more dense medium (e.g. air to glass), r < i (bends towards the normal)
  • If light travels from a more dense to a less dense medium (e.g. glass to air), r > i (bends away from the normal)

  • The angles of incidence and refraction are related by an equation known as Snell's Law:

n space equals space fraction numerator sin space i over denominator sin space r end fraction

  • Where:
    • n = the refractive index of the material
    • i = angle of incidence of the light (°)
    • r = angle of refraction of the light (°)

  • 'Sin' is the trigonometric function 'sine' which is on a scientific calculator

Worked example

A ray of light enters a glass block of refractive index 1.53 making an angle of 15° with the normal before entering the block.

Calculate the angle it makes with the normal after it enters the glass block.

Answer:

Step 1: List the known quantities

  • Refractive index of glass, n = 1.53
  • Angle of incidence, i = 15°

Step 2: Write the equation for Snell's Law

n space equals space fraction numerator sin space i over denominator sin space r end fraction

Step 3: Rearrange the equation and calculate sin (r)

sin space r space equals space fraction numerator sin space i over denominator n end fraction

sin space r space equals space fraction numerator sin open parentheses 15 degree close parentheses over denominator 1.53 end fraction space equals space 0.1692

Step 4: Find the angle of refraction (r) by using the inverse sin function

r = sin–1 (0.1692) = 9.7 = 10°

Examiner Tip

Important: (sin i / sin r) is not the same as (i / r). Incorrectly cancelling the sin terms is a very common mistake!

When calculating the value of i or r start by calculating the value of sin i or sin r.

You can then use the inverse sin function (sin–1 on most calculators by pressing 'shift' then 'sine') to find the angle.

One way to remember which way around i and r are in the fraction is remembering that 'i' comes before 'r' in the alphabet, and therefore is on the top of the fraction (whilst r is on the bottom).

Additionally, make sure your calculator is in degrees mode, not radians mode, when you are given i and r in  degrees.

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Dan MG

Author: Dan MG

Expertise: Physics

Dan graduated with a First-class Masters degree in Physics at Durham University, specialising in cell membrane biophysics. After being awarded an Institute of Physics Teacher Training Scholarship, Dan taught physics in secondary schools in the North of England before moving to SME. Here, he carries on his passion for writing enjoyable physics questions and helping young people to love physics.