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Wize University Physics Textbook (Master) > Geometric Optics

Total Internal Reflection

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Total Internal Reflection




Total internal reflection occurs when the refracted ray doesn't reach the second medium, instead is completely reflected inside the original medium.

Wize Concept
This can only happen when light goes from a higher index of refraction (denser medium) to a lower index of refraction (less dense medium). That is, n1>n2n_1>n_2.


The critical angle θc\theta_c is the incident angle that results in a refraction angle of 90°90\degree, for which the refracted ray is along the boundary between the media:

 sin⁡θc=n2n1 \boxed{\ \sin\theta_c=\dfrac{n_2}{n_1} \ }

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For all incident angles greater than the critical angle, total internal reflection will happen.


Exam Tip
  • If θ1<θc\theta_1<\theta_c we still have regular refraction.
  • If θ1>θc\theta_1>\theta_c we have total internal reflection, and no refraction.

Determine the critical angle of a diamond (n=2.4n=2.4) to air interface. What is the critical angle for a diamond to glass (n=1.5n = 1.5) interface? (Answer in degrees)

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Practice: Rock Under Water

A large rock sits in the bottom of a 2.8 m deep salt water swimming pool (n = 1.36). A swimming child looks downwards and sees that as she crosses the pool, there is only a small region that she can swim within surrounding the rock in which she can see the rock. Determine the daimeter of the region. Give answer in metres.