refraction, critical angle and total internal reflection

We met refraction during the National 5 course.  At Higher level, we are interested in the relationship between the angles of incidence θi and refraction θr.

Snell’s law tells us that

n_1\sin \theta_i = n_2 \sin \theta_r

Usually material 1 is air, and so n_1 = 1.  This simplifies Snell’s law to

\sin \theta_i = n \sin \theta_r

where n is the absolute refractive index of material 2.  Since the refractive index is equal to the ratio of the ray’s speed v in materials 1 & 2 and also equal to the ratio of the wave’s wavelength λ in materials 1 & 2, we can show that

 n = \displaystyle {{{\sin \theta_i} \over  {\sin \theta_r}}} = \displaystyle {v_1 \over v_2} = \displaystyle {\lambda_1 \over \lambda_2}

Read more about Snells’s law here.

total internal reflection

total internal reflection from mr mackenzie on Vimeo.
The critical angle \theta_c and refractive index n are related by

\sin \theta_c = \displaystyle {1 \over n }

Here are some applications of total internal reflection here.  You can test your knowledge of refraction with this interactive simulation.

I have attached a pdf with some notes and questions on refraction, total internal reflection and critical angle.