Fresnel Diffraction Homework: Annular Ring Irradiance

[grothem]

Homework Statement

A point source of monochromatic light (500 nm) is 50 cm from an aperture plane. The detection point is located 50 cm on the other side of the aperture plane.

a) The transmitting portion of the aperture plane is an annular ring of inner radius .5 mm and outer radius .935 mm. What is the irradiance at the detector relative to the irradiance there for an unobstructed wavefront?

b) Answer the same question if the outer radius is 1.00 mm

c) How many half-period zones are included in the annular ring in each case?

Homework Equations

Rn = (n*ro*lambda)^1/2

The Attempt at a Solution

I don't even know where to start on this problem. I know R1 and R2 but I don't know how I can go from there to determine the irradiance. I know that irradiance is proportional to the electric field squared, but I'm still confused by this problem.

 

[mark726]

Thank you for your post. I would like to help you understand this problem. Let's start by breaking it down into smaller parts.

First, let's define some terms. Irradiance, also known as intensity, is the amount of energy per unit area per unit time. It is usually denoted by the symbol E and has units of watts per square meter (W/m^2). In this problem, we are dealing with monochromatic light, which means the light has a single wavelength of 500 nm.

Now, let's look at the setup described in the problem. We have a point source of monochromatic light located 50 cm away from an aperture plane. The detection point is also 50 cm away from the aperture plane, on the other side. The transmitting portion of the aperture plane is an annular ring with inner radius 0.5 mm and outer radius 0.935 mm (in part a) and 1.00 mm in part b).

To solve this problem, we need to use the equation for irradiance, which is given by E = (c/4π) * (E0)^2, where c is the speed of light and E0 is the electric field amplitude. We also need to use the equation for the radius of the nth half-period zone, which is given by Rn = (n*ro*λ)^1/2, where n is the number of half-period zones, ro is the outer radius of the aperture, and λ is the wavelength of the light.

Now, let's look at part a) of the problem. We are asked to find the irradiance at the detector relative to the irradiance for an unobstructed wavefront. This means we need to find the ratio of the irradiance at the detector to the irradiance for an unobstructed wavefront.

To do this, we first need to find the number of half-period zones included in the annular ring. To do this, we can use the equation for the radius of the nth half-period zone. In this case, we are given the outer radius of the aperture (0.935 mm) and the wavelength of the light (500 nm). Plugging these values into the equation, we get Rn = (n*0.935*10^-3*500*10^-9)^1/2 = n*0.000154 m.