A 1.20-cm-tall object is 50.0 cm to the left of a converging...

A 1.20-cm-tall object is 50.0 cm to the left of a converging lens of focal length 40.0 cm. A second converging lens, this one having a focal length of 60.0 cm, is located 300.0 cm to the right of the first lens along the same optic axis. (a) Find the location and height of the image (call it $I_1$) formed by the lens with a focal length of 40.0 cm. (b) $I_1$ is now the object for the second lens. Find the location and height of the image produced by the second lens. This is the final image produced by the combination of lenses.

Key Concepts

Optical Sign Conventions

A consistent set of sign conventions is essential in optical calculations to correctly interpret distances and directions. For instance, distances measured in the direction of incident light are typically taken as positive, while those measured opposite to it are negative. These conventions help in determining whether images formed are real or virtual, as well as their orientations.

Sequential Imaging Through Multiple Lenses

When dealing with systems that incorporate more than one lens, the image formed by the first lens becomes the object for the subsequent lens. This sequential processing is crucial in complex optical systems, as each lens’s calculations must account for the position and size of the intermediate image to predict the final image characteristics.

Thin Lens Equation

This fundamental relation in geometrical optics relates the focal length of a thin lens to the object distance and the image distance through the formula 1/f = 1/d_o + 1/d_i. It is used to determine the position where an image will form given an object’s location relative to the lens, and is equally applicable to both magnifying and reducing systems.

Magnification

Magnification describes the ratio of the image height to the object height and is given by m = -d_i/d_o. This concept not only tells us how much larger or smaller the image is compared to the object but also indicates the orientation of the image, with a negative value signifying an inverted image.