C
CraftExam
medium difficulty9 min

Refraction, Snell's Law and Total Internal Reflection

Refraction is the bending of light when it passes obliquely from one transparent medium to another because its speed changes. Total internal reflection is the complete reflection of light back into a denser medium when the angle of incidence exceeds the critical angle.

In one line: TIR needs two checks: denser to rarer, then angle greater than critical.

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Understand it

  • Snell's law connects the angles of incidence and refraction with the refractive indices of the two media.
  • When light travels from a denser medium to a rarer medium, the refracted ray bends away from the normal.
  • At the critical angle, the refracted ray grazes the interface.
  • For angles greater than the critical angle, no refracted ray emerges and total internal reflection occurs.
  • This explains optical fibres, sparkling of diamonds and mirage-like effects at school level.

Example

In an optical fibre, light repeatedly undergoes total internal reflection inside the core, allowing signals to travel along curved paths with low loss.

Formula and rule

Snell's law: n1 sin θ1 = n2 sin θ2.

Critical angle for denser medium 1 to rarer medium 2: sin θc = n2/n1, where n1 > n2.

Refractive index is dimensionless; angles are measured from the normal, not from the surface.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

Light travels from glass of refractive index 1.5 to air of refractive index 1.0. sin θc = n2/n1 = 1.0/1.5 = 0.667.

  1. 1Therefore θc is about 41.8 degrees.
  2. 2If the incidence angle in glass is 50 degrees, total internal reflection occurs because 50 degrees is greater than 41.8 degrees.

Method you can reuse

Identify denser and rarer media; confirm light travels denser to rarer; apply sin θc = n2/n1; compare the given incidence angle with θc; state whether refraction or TIR occurs.

Visual tip

Diagram should show interface, normal, incident ray in denser medium, refracted ray bending away from normal, critical-angle case with refracted ray along interface, and TIR case with reflected ray inside the denser medium.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What two conditions are necessary for total internal reflection?

Think first, then show answer
The light must travel from an optically denser medium to an optically rarer medium, and the angle of incidence in the denser medium must be greater than the critical angle for the two media.

Common wrong answer

A common wrong answer is sin θc = n1/n2, which can give a value greater than 1 and is physically impossible.

Don't mix this up

Students write total internal reflection for any reflection at a boundary. It occurs only from denser to rarer medium and only when the incidence angle is greater than the critical angle.

Exam tip

For TIR questions, check the direction of travel first. If light is going from rarer to denser medium, TIR cannot occur.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Questions ask for critical angle calculation, conditions for TIR, optical fibre working, and comparison between ordinary reflection and total internal reflection.
  1. 1

    Enough for 1 mark

    Refraction is the bending of light when it passes obliquely from one transparent medium to another because its speed changes. Total internal reflection is the complete reflection of light back into a denser medium when the angle of incidence exceeds the critical angle.

  2. 2

    Add for 2 marks

    Example: In an optical fibre, light repeatedly undergoes total internal reflection inside the core, allowing signals to travel along curved paths with low loss.

  3. 3

    Add for 3 marks

    Snell's law connects the angles of incidence and refraction with the refractive indices of the two media.

Practice

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