When light passes from a more dense to a less dense substance, (for example passing from water into air), the light is refracted (or bent) away from the normal.

My question, is there any theory that i can say precisely why light go away from normal or get closed to the normal.


Yes. The boundary conditions for Maxwell's equations gets you this. This reasoning is much more simple than it sounds.

High refractive index means phasefronts of a plane wave are nearer together than for a low refractive index. When the waves in both mediums line up at the interface, the spacing between the intersection of the phasefronts and the interface must be the same so that the transverse components of the electromagnetic field can be continuous across the interface.

The only way this can happen is if the direction of the transmitted wave bends relative to that of the incident wave. If the transmitted into medium is denser, with more closely spaced wavefronts, this means that the transmitted wavevector must be bent away from the interface, i.e. bent towards the unit normal.

My answer here gives a diagram that completes this reasoning.


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