Far Field lens Imaging…Does k-wave number follow arc length equation?

In summary: This result is useful for understanding the behavior of light in lens systems and can also be confirmed experimentally. In summary, the distance subtended by a light ray in a lens-less system is proportional to the distance to the screen and the angle of the ray. However, when a lens is added, the distance subtended becomes a function of the focal length and angle. In the case of imaging in the far field region, the k-space subtended is proportional to k-naught and theta, and this can be proven using the equations of geometrical optics.
  • #1
jasonpatel
35
0
If we are imaging light in the far field region. We have three situations/relations (illustrated below):

Arc Length: We know the distance subtended (S) by the light ray in a lens-less system will be proportional to R (distance to the screen) and theta; simple, especially if theta is very small.

Put a lens in the system (focused at infinity) and the distance subtended (Y) becomes a function of the focal length and theta. I confirmed this result using matrix optics!

Now, the part in question:

Considering the same lens system, can we say that because the imaging plane images the Far Field Distribution (k-space) and essentially angles of the incoming light can we say that the k-space subtended (dk) is proportional to k-naught and theta (see equation below)?? If so how do I go about proving this?!
Any help would be greatly appreciated!
HWFwB.jpg
 
Science news on Phys.org
  • #2
Yes, you can say that the k-space subtended (dk) is proportional to k-naught and theta. The proof of this would involve using the equations of geometrical optics to calculate the ray angles at the imaging plane and the focal length of the lens system. From these equations, you can derive the expression for dk and show that it is proportional to k-naught and theta.
 

1. What is a Far Field lens and how does it work?

A Far Field lens is an optical device that can capture images of objects at a distance. It works by using a series of lenses to focus light from a distant object onto a detector, which creates an image of the object. The lenses are designed to correct for distortions caused by the curvature of the Earth's surface, allowing for clear and accurate images to be captured.

2. What is the difference between Far Field lens imaging and Near Field lens imaging?

Far Field lens imaging is used to capture images of objects at a distance, typically greater than the wavelength of the light being used. Near Field lens imaging, on the other hand, is used to capture images of objects that are closer to the lens, typically within the near field region of the light. Far Field lens imaging tends to produce higher resolution images, while Near Field lens imaging is better for studying the details of small objects.

3. How does the k-wave number relate to the arc length equation in Far Field lens imaging?

The k-wave number, also known as the wave vector, is a mathematical quantity that describes the spatial frequency of a wave. In Far Field lens imaging, the k-wave number is used to calculate the arc length of the wavefront, which is the distance between the lens and the object being imaged. This is important because the arc length affects the resolution and quality of the image produced.

4. Can Far Field lens imaging be used for all types of light, such as infrared or ultraviolet?

Yes, Far Field lens imaging can be used for all types of light, as long as the lens is designed to focus that specific wavelength. Different lenses are used for different types of light, as they are designed to correct for the unique properties of each wavelength. For example, an infrared lens would be used to capture images of objects that emit infrared light, while an ultraviolet lens would be used for objects that emit ultraviolet light.

5. Is Far Field lens imaging affected by atmospheric conditions?

Yes, atmospheric conditions can have an impact on Far Field lens imaging. For example, in conditions with high levels of humidity, light can scatter and distort the image being captured by the lens. This is why many scientific instruments and telescopes are located in areas with low humidity, such as deserts or high-altitude locations, to minimize these effects and improve the quality of the images captured.

Similar threads

I Using simple lenses to image AFM Probes
    • Optics
Replies
10
Views
1K
I Image appears outside of q -- Lens Maker's Equation confusion
    • Optics
Replies
17
Views
2K
What are the key considerations for imaging with a condenser fresnel lens?
    • Optics
2
Replies
58
Views
5K
Should Approved Sign Conventions be Applied in Optics Problems Using Lens and Mirror Equations?
    • Optics
Replies
13
Views
9K
Direction or angle independent image formation in lens
    • Optics
Replies
1
Views
1K
Inserting thick lenses into a thin lens system and deducing values
    • Introductory Physics Homework Help
Replies
1
Views
960
Thin lens approximation and Apparent depth
    • Optics
Replies
20
Views
3K
Understanding the Thin & Gaussian Lens Equations
    • Optics
Replies
1
Views
2K
Image seen by human eye through a convex lens
    • Optics
Replies
2
Views
1K
Wave Physics - Optics - Effective Focal Length
    • Introductory Physics Homework Help
Replies
12
Views
3K

Hot Threads

Recent Insights

Back
Top