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Snell's Law (Edexcel IGCSE Physics)

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Katie M

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Katie M

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Edexcel PhysicsEdexcel Science (Double Award): Physics

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Snell's law

  • The angles of incidence and refraction are related to the refractive index of a medium 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

  • You can revise the concept of refraction using the revision notes Reflection & refraction

A formula triangle can help rearrange the snell's law equation

Snell triangle (2), IGCSE & GCSE Physics revision notes

Snell's law formula triangle

  • For more information on how to use a formula triangle refer to the revision note on Speed

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):

refractive space index comma space n space equals space fraction numerator speed space of space light space in space straight a space vacuum over denominator speed space of space light space in space material end fraction

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

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 space over denominator sin space r end fraction

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

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

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

sin space r italic space equals space 0.1692

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

r space equals space sin to the power of – 1 end exponent space left parenthesis 0.1692 right parenthesis space equals space 9.7 space equals space 10 degree

Examiner Tips and Tricks

Important: in snell's law fraction numerator sin space i over denominator sin space r end fraction is not the same as i over r. Incorrectly cancelling the sin terms is a 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).

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    Katie M

    Author: Katie M

    Expertise: Physics

    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.