Why does parallel light focus on the focal plane at angle θ through a thin lens?

[brianeyes88677]

Why does parallel light focus on the focal plan when enters a thin lens at an angle θ?
How to proof that mathematically?

 

[berkeman]

Why does parallel light focus on the focal plan when enters a thin lens at an angle θ?
How to proof that mathematically?

Does the Thin Lens page at wikipedia help? http://en.wikipedia.org/wiki/Thin_lens

 

[brianeyes88677]

I need the proof that the parallel light isn't perpendicular to the lens.

 

[blue_leaf77]

The proof can easily be done using the ray transfer matrices. In case you are not familiar with this term yet, navigate to this http://en.wikipedia.org/wiki/Ray_transfer_matrix_analysis
In describing focusing of a collimated beam (parallel rays) using such matrices, one uses the matrix product between thin lens matrix and free space propagation matrix in the order that the thin lens matrix is on the right. This order corresponds to the encounter of the ray bundle with the lens first, then propagate further behind it to reach the focal plane. The resulting matrix have the element A=0. This kind of ray transfer matrix is termed as having focusing behavior, and you will see at the end of your calculation that the heights of all rays at the focal plane are equal, which physically means they are being focused.