A 2.0-cm-tall object is 20 cm to the left of a lens with a...

A 2.0-cm-tall object is $20 \mathrm{cm}$ to the left of a lens with a focal length of $10 \mathrm{cm} .$ A second lens with a focal length of $5 \mathrm{cm}$ is $30 \mathrm{cm}$ to the right of the first lens. a. Use ray tracing to find the position and height of the image. Do this accurately with a ruler or paper with a grid. Estimate the image distance and image height by making measurements on your diagram. b. Calculate the image position and height. Compare with your ray-tracing answers in part a.

A 2.0-cm-tall object is $20 \mathrm{cm}$ to the left of a lens with a focal length of $10 \mathrm{cm} .$ A second lens with a focal length of $5 \mathrm{cm}$ is $30 \mathrm{cm}$ to the right of the first lens.
a. Use ray tracing to find the position and height of the image. Do this accurately with a ruler or paper with a grid. Estimate the image distance and image height by making measurements on your diagram.
b. Calculate the image position and height. Compare with your ray-tracing answers in part a.

Key Concepts

Magnification

Magnification is the measure of the relative size of the image compared to the object, defined as m = -di/do. The negative sign indicates image inversion, and its absolute value reveals whether the image is magnified or diminished relative to the object.

Sequential Lens Systems

In optical systems with multiple lenses, the image produced by one lens becomes the object for the next. Analyzing such systems requires sequential application of the thin lens equation and careful tracking of object and image distances between the components, ensuring that sign conventions and relative distances are correctly maintained.

Ray Tracing in Geometric Optics

Ray tracing is a graphical method used in optics to determine the formation and characteristics of images by drawing the propagation of selected rays through optical systems. It involves the use of principal rays—such as the ray parallel to the optical axis, the ray passing through the center of the lens, and the ray through the focal point—to accurately locate images and assess their size and orientation.

Thin Lens Equation and Sign Conventions

The thin lens equation, 1/f = 1/do + 1/di, connects the focal length (f) of a lens with the object distance (do) and the image distance (di), enabling the calculation of where an image will form. Applying proper sign conventions is critical for correctly identifying whether an image is real or virtual, and whether it is inverted or upright.