Why does light bend when it passes through different materials?

Light bends due to the difference in refractive index to fulfill the property that light travels the fastest way from point a to point b.

A good example i heard in a lecture was that of a life guard at a beach. The lifeguard can run significantly faster than he can swim. If a person is in the water in distress x meters along the beach and y meters into the water away from the life guard, the life guard is not going to run first x meters on the beach and then y meters in the water, but he will instinctively run at an angle and cross the water at some point between them.

When a wave interacts with a thicker medium for example it will slow down inside this medium. When the wave approaches the interface at an angle, part of the wave will slow down before the other parts and this is one way of imagining why it tilts. This change in direction and speed is governed by the law of refraction.

$$ \frac{\sin\theta_1}{\sin\theta_2} = \frac{v_1}{v_2}$$

You also have to keep in mind that what anna v said, this theory of refraction is composed of a different set of physics and that classical electromagnetic theory is enough to fully describe this phenomenon and that quantum physics is not required.

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