Understanding the Focal Plan of Parallel Light Through a Thin Lens

In summary, the parallel light focuses on the focal plane when entering a thin lens at an angle θ due to the use of ray transfer matrices. The order of the matrices, with the thin lens matrix on the right, allows for the ray bundle to encounter the lens first and then propagate to reach the focal plane. This results in a matrix with a value of A=0, indicating a focusing behavior and causing all rays to be focused at equal heights at the focal plane. For a mathematical proof, one can refer to the Thin Lens page on Wikipedia or use the ray transfer matrix analysis method.
  • #1
brianeyes88677
13
0
Why does parallel light focus on the focal plan when enters a thin lens at an angle θ?
How to proof that mathematically?
 
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  • #2
brianeyes88677 said:
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

:smile:
 
  • #3
I need the proof that the parallel light isn't perpendicular to the lens.
 
  • #4
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.
 

1. What is the focal plan of parallel light?

The focal plan of parallel light is the point at which a beam of parallel light rays converge after passing through a thin lens. This point is also known as the focal point or focal length of the lens.

2. How is the focal plan of parallel light determined?

The focal plan of parallel light is determined by the curvature of the lens and the refractive index of the material it is made of. The greater the curvature and refractive index, the shorter the focal length will be.

3. Why is understanding the focal plan of parallel light important?

Understanding the focal plan of parallel light is important in various fields such as optics, photography, and astronomy. It allows us to accurately predict where a parallel beam of light will converge and how it will be affected by a thin lens.

4. Can the focal plan of parallel light be altered?

Yes, the focal plan of parallel light can be altered by changing the properties of the lens such as its curvature or refractive index. This can be done by using different materials or shapes for the lens.

5. How does the focal plan of parallel light differ from the focal plan of diverging light?

The focal plan of parallel light is the point where a beam of parallel light rays converge, while the focal plan of diverging light is the point where a beam of diverging light rays appear to originate from when passing through a lens. They are essentially opposite concepts.

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