What is the Correct Calculation for Spherical Aberrations in a Lens?

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In summary, the incident collimated light beam on a plane side of a lens with an index of refraction of 1.5, a diameter of 50mm, and a radius of curvature of 40mm results in a virtual image at infinity. Using the equations for refraction on a plane and spherical surface, the image distance is found to be 80mm and the spherical wave aberration is calculated to be -0.858mm. The discrepancy with the given answer is due to an error in using the index of refraction in the calculation of the spherical wave aberration.
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Xyius
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Homework Statement


A collimated light beam is incident on the plane side of a of index 1.5, diameter 50mm, and radius 40mm. Find the .

Homework Equations


Refraction in a plane surface:
[tex]s'=\frac{-n_2}{n_1}s[/tex]
Refraction on a spherical surface:
[tex]\frac{n_1}{s}+\frac{n_2}{s'}=\frac{n_2-n_1}{R}[/tex]
Spherical Wave Aberrations:
[tex]a(Q)= \frac{h^4}{8} \left[ \frac{n_1}{s} \left( \frac{1}{s}+\frac{1}{R}\right)^2 + \frac{n_1}{s'} \left( \frac{1}{s'}-\frac{1}{R}\right)^2 \right][/tex]

R=Radius of curvature
s=Object distance
s'=Image distance
n=index of refraction

The Attempt at a Solution


So the light is traveling in a straight beam incident on the plane surface. By equation 1, the image distance is virtual and at infinity. so [itex]s'=-\infty mm[/itex]. I then use this value for the calculation of the image of a spherical surface using equation 2. Plugging everything in, I get a distance of 80mm. So s'=80mm.

I then used equation 3 to get the spherical wave aberration and used a height of 25mm since the lens is 50mm in diameter. (Also, R<0 since it is a concave surface from left to right.) I got an aberration of -1.29mm. The book says the correct answer is -0.858mm.

What am I doing wrong? :(?

EDIT: Figured it out! I used 1.5 for the index in equation 3 instead of 1.
 
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What is a spherical aberration?

Spherical aberration is an optical phenomenon that causes light rays to be focused at different points when passing through a spherical lens or mirror, resulting in a blurred or distorted image.

What causes spherical aberrations?

Spherical aberrations are caused by the curvature of a spherical surface, which causes light rays passing through the edges of the lens to focus at different points than those passing through the center.

What are the effects of spherical aberrations?

The main effect of spherical aberrations is a decrease in image quality, typically seen as blurring or distortion around the edges of an image. This can be especially noticeable in telescopes and microscopes.

How can spherical aberrations be corrected?

Spherical aberrations can be corrected by using a lens or mirror with a non-spherical shape, such as a parabolic or aspherical surface. This helps to focus all incoming light rays to a single point, resulting in a clearer image.

Are spherical aberrations present in all optical systems?

Yes, spherical aberrations are present in all optical systems that use spherical lenses or mirrors. However, the amount of aberration can vary depending on the quality and design of the optical system.

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