When the media have the same index of refraction, no refraction occurs because the speed of light is the same in both media. As a result, the light rays do not bend when passing from one medium to the other. This can be understood using Snell's law, which describes the relationship between the angle of incidence, angle of refraction, and the indices of refraction of the two media.

Snell's law is given by:

$$n_1 \sin\theta_1 = n_2 \sin\theta_2$$

where:

- \(n_1\) and \(n_2\) are the indices of refraction of the first and second media, respectively

- \(\theta_1\) is the angle of incidence (the angle between the incident light ray and the normal to the surface at the point of incidence)

- \(\theta_2\) is the angle of refraction (the angle between the refracted light ray and the normal to the surface at the point of refraction)

If \(n_1 = n_2\), then \(\sin\theta_1 = \sin\theta_2\). This means that the angle of incidence is equal to the angle of refraction, and the light ray does not bend when passing from one medium to the other.

In summary, no refraction occurs when the media have the same index of refraction because the speed of light is the same in both media, and as a consequence, the light rays do not bend when passing from one medium to the other.