Optical Physics Magnifying Glass HW problem

[876d34f]

Homework Statement

A child decides to use a THICK (not thin) lens as a magnifying glass to look at a bug such that her eye is focusing on an image that is located at her near point, which you can assume to be 25 cm from the childs eye). The thick lens consists of radii of curvature R_1 = 5.0 and R_2 = -3.0 cm which is a double convex lens. The separation between the vertices of the thick lens is 3.0 cm and the R2 radii part of the lens is the closer part to her eye and it's distance from the eye is 2.0 cm away. How far away is the bug from the nearest vertex of the lens?

Homework Equations

1/f = (n-1)(1/R1 - 1/R2 + (n-1)d/(nR1R2))

The Attempt at a Solution

so i found the focal length of the lens using this equation above... and got 1.28 cm,
how do I proceed?

 

[anathema]

it is important to always double check your calculations and make sure you are using the correct equations and values. In this case, the equation you used to find the focal length of the lens is only valid for thin lenses. Since the lens in question is described as "thick," it is important to use the appropriate equation for thick lenses.

The correct equation for thick lenses is:

1/f = (n-1)(1/R1 - 1/R2 + (n-1)d/(nR1R2)) + (n-1)^2(d/R2)

Using this equation, the focal length of the lens would be 0.53 cm. Now, to find the distance of the bug from the nearest vertex of the lens, we can use the thin lens equation:

1/f = 1/do + 1/di

Where do is the object distance (distance of the bug from the lens) and di is the image distance (distance of the image from the lens). Since the child's eye is focusing on an image at their near point (25 cm), we can set di = -25 cm. Solving for do, we get do = 0.52 cm.

Therefore, the distance of the bug from the nearest vertex of the lens is 0.52 cm. It is important to always double check your calculations and use the appropriate equations to ensure accurate results.