Finding Image for a Thick bi-concave Lens

[davydany]

Homework Statement

A bi-concave lens (n=2) has radii of 15cm and 25cm, and an axial thickness of 6-cm. Use the thin-lens equation to see how far off it is in determining the final image location.

Homework Equations

n1/so + n2/si = (n2 – n1)/R;

(n-1)(1/R1 – 1/R2) = 1/f

The Attempt at a Solution

I got the focal length of the lens to be 28.846 using the 2nd equation above.
(2-1)[1/15 - 1/25 + ((2-1)*6) / (2*15*25))] = 28.846

I found h1 and h2 to be -3.46 and -5.77, respectively.

I realize that So = 10cm + h1 = 10 + 3.46 = 13.46

I plugged this into the Len's Maker's Equation (1/so + 1/si = 1/f) and found that si = 25.24.

I had a couple of questions with this:

1. Do thick concave lens have first and second principle points (h1 and h2)?
2. The axial thickness is 6cm. However, h2 is -5.77 and h1 is -3.46. It seems like they are crossing each other and h2 is found where h1 is supposed to be and vice versa.
3. Am I approaching this correct?

 

[anathema]

Your approach seems to be correct. However, there are a few things to consider when using the thin-lens equation to determine image location for a bi-concave lens.

Firstly, it is important to note that the thin-lens equation is only an approximation and may not give a completely accurate result for thick lenses. This is because the thin-lens equation assumes that the lens is infinitely thin, which is not the case for a bi-concave lens with an axial thickness of 6cm.

Secondly, the thin-lens equation assumes that the lens is symmetric, meaning that the radii of curvature on either side of the lens are equal. In the case of a bi-concave lens, this is not true as the radii of curvature are 15cm and 25cm. This can lead to some discrepancies in the results obtained using the thin-lens equation.

To answer your specific questions, thick lenses do have first and second principle points, but they are not always easy to determine. In the case of a bi-concave lens, the first principle point is located on the left side of the lens, while the second principle point is located on the right side. The axial thickness of the lens can affect the location of these points, which is why they appear to be crossing each other in your calculations.

In conclusion, while your approach is correct, it is important to keep in mind the limitations of the thin-lens equation when dealing with thick lenses. It may be helpful to use other methods, such as ray tracing or the matrix method, to get a more accurate result for image location in this case. I hope this helps clarify your understanding.