Explain refraction of plane wave with a thin prism.

Explanation

The figure shows the parallel beam is incident on a prism at a instant and its corresponding plane wavefront `A_(1)B_(1). A_(1)B_(1)` is normal to rays and emergent beam is shown by `A_(2)B_(2)`.
Here the length of the path from `B_(1)` to `B_(2)` is greater then the length of the path from `A_(1)` to `A_(2)`
In fact, the path from `A_(1)` to `A_(2)` in prism is larger than the path from `B._(2)` to `B._(2)`
The velocity of light in prism is less than the velocity in air hence it takes longer time for the light to go from `A_(1)` to `A_(2)` As a result, `A_(2)` is lagging behind point `B_(2)`. So the emergent wavefront is slightly tilted.