[College Electrical Engineering/Physics] Waves & Lens

In summary, when a plane wave is transmitted through a thin lens of focal length f in a direction parallel to the axis, it is converted into a paraboloidal wave centered about a point at a distance f from the lens. This can be shown mathematically by analyzing the behavior of off-axis rays impinging on the focal plane, which forms a parabola in 2 dimensions. This argument can then be extended to 3 dimensions.
  • #1
DerpyDalek
1
0

Homework Statement



Show that when a plane wave is transmitted through a thin lens of focal length f in a direction parallel to the axis of the lens, it is converted into a paraboloidal wave (the Fresnel approximation of a spherical wave) centered about a point at a distance f from the lens.

Homework Equations



U(r) = (Ao/z)exp(-jkz)exp[-jk(x^2 + y^2)/2z]

The Attempt at a Solution



I am having trouble determining how to best set up this problem, i understand visually why this occurs as a plane wave contacts a thin lens and transforms but am having problems seeing the math to "prove" that this is what occurs.

Currently looking into how the lens affects the speed of light as it passes through each point of the lens at the front of the wave
 

Attachments

  • 20140212_050359_resized.jpg
    20140212_050359_resized.jpg
    31.4 KB · Views: 939
Last edited:
Physics news on Phys.org
  • #2
Use 2 dimensions to start. You should be able to show by analytic geometry that the locus of off-axis rays impinging on the focal plane is a parabola. Then extend the argument to 3 dimensions.
 

FAQ: [College Electrical Engineering/Physics] Waves & Lens

1. What are electromagnetic waves?

Electromagnetic waves are a form of energy that can travel through space and carry energy from one place to another. They consist of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of wave propagation.

2. What is the difference between mechanical and electromagnetic waves?

Mechanical waves require a medium, such as air or water, to travel through, while electromagnetic waves can travel through a vacuum. Mechanical waves also have a characteristic frequency and wavelength, while electromagnetic waves have a continuous spectrum of frequencies.

3. How do lenses work?

Lenses work by refracting light, causing it to change direction as it passes through the lens. This refraction is due to the difference in density between the lens material and the surrounding medium. Convex lenses converge light rays, while concave lenses diverge them.

4. What is the difference between a converging and a diverging lens?

A converging lens, also known as a convex lens, has a thicker center and causes light rays to converge at a focal point. A diverging lens, also known as a concave lens, has a thinner center and causes light rays to diverge.

5. How are lenses used in everyday life?

Lenses have a wide range of applications in everyday life, from corrective eyeglasses and contact lenses to cameras and telescopes. They are also used in medical devices, such as microscopes and endoscopes, and in various industrial processes, such as laser cutting and welding.

Similar threads

How to find the center of a paraboloidal wave
Replies
1
Views
4K
How Can a Lens Maintain Constant Thickness and Still Focus Light?
Replies
11
Views
3K
Paraboloidal Wave Conversion via Biconvex Lens
Replies
1
Views
4K
Inserting thick lenses into a thin lens system and deducing values
Replies
1
Views
1K
What are the key considerations for imaging with a condenser fresnel lens?
2
Replies
58
Views
6K
I How Can I Build an Effective DIY Helmet-Mounted HUD?
Replies
19
Views
1K
Geometrical optics - lens floating in mercury
Replies
1
Views
3K
Image with an Plano-Convex lens
Replies
7
Views
2K
Find Focal Length of Biconcave Lens with Galilean Telescope
Replies
1
Views
6K
Double slits and convex lens interference
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top