Fresnel Biprism Equation Derviation-

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In summary, the Fresnel Biprism equation is derived from the simple lens formula, with the separation of images related to the ratio of image and object distances. The equation d = (d1 * d2)^1/2 represents the actual separation of the virtual slits and can be calculated using the ratio of image and object distances. The process for deriving this equation involves considering the first and second lens positions and working with the ratios of image and object distances.
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Fresnel Biprism Equation Derviation- please help!

I recently did the Fresnel Biprism Experiment in order to calculate the wavelength of sodium light. As part of my write up I am to show the derviation of the formula d = (d1 * d2)^1/2 where d = actual separation of the virtual slits. Basically I don't have any idea how to derive this, all I know that it is supposed to come from the simple lens formula...does anyone have any idea how to derive this?? Any help would be greatly appreciated!
 
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I am looking at http://www.uow.edu.au/eng/phys/200labs/phys215/fresnel.pdf [Broken]

The separation of the images at a given lens position is related to the separation of the virtual sources like the ration of image to object distances.

Let u = image distance
let v = object distance

In the first lens position you have

[tex] \frac c {c_1} = \frac u v [/tex]

At the second lens position you have
[tex] \frac c {c_2} = \frac v u[/tex]

Can you work it out from there?
 
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Thanks, I just didnt really know where to start, but looking at that it helps a lot, as I know where to work from. Thanks again!
 

1. What is the Fresnel Biprism Equation and why is it important?

The Fresnel Biprism Equation is a mathematical equation that describes the interference pattern produced by a biprism, which is a type of optical device used to create interference fringes. It is important because it allows scientists to accurately predict and analyze the interference patterns produced by biprisms, which has applications in fields such as optics, spectroscopy, and interferometry.

2. How is the Fresnel Biprism Equation derived?

The Fresnel Biprism Equation is derived from the principles of wave optics and interference. It involves using the Huygens-Fresnel principle to calculate the amplitude of the interfering waves at a specific point on the screen, taking into account the path differences between the two waves.

3. What are the key variables in the Fresnel Biprism Equation?

The key variables in the Fresnel Biprism Equation are the wavelength of light, the distance between the biprism and the screen, the distance between the two virtual sources created by the biprism, and the angle of incidence of the light on the biprism. These variables determine the shape and spacing of the interference fringes.

4. How does the Fresnel Biprism Equation change with different parameters?

The Fresnel Biprism Equation is a complex equation that involves trigonometric functions and can be affected by changes in any of the key variables. For example, increasing the distance between the biprism and the screen will result in wider interference fringes, while changing the angle of incidence will alter the spacing between the fringes.

5. Are there any limitations to the Fresnel Biprism Equation?

Like any mathematical model, the Fresnel Biprism Equation has its limitations. It assumes ideal conditions, such as a monochromatic light source and perfectly parallel incident light, which may not always be the case in real-world experiments. Additionally, it does not account for the effects of diffraction, which can impact the accuracy of the predicted interference pattern.

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