Verify the locations and sizes of the images formed by the...

Verify the locations and sizes of the images formed by the two lenses in Fig. $24.1 \mathrm{~b}$ using the lens equation and the following data: $f_{1}=+4.00 \mathrm{~cm}, f_{2}=-2.00 \mathrm{~cm}, s=$ $8.00 \mathrm{~cm}$ (where $s$ is the distance between the lenses), $p_{1}$ $=+6.00 \mathrm{~cm}$, and $h=2.00 \mathrm{~mm} .$ (Note that the vertical scale is different from the horizontal scale.)

Verify the locations and sizes of the images formed by the two lenses in Fig. $24.1 \mathrm{~b}$ using the lens equation and the following data: $f_{1}=+4.00 \mathrm{~cm}, f_{2}=-2.00 \mathrm{~cm}, s=$
$8.00 \mathrm{~cm}$ (where $s$ is the distance between the lenses), $p_{1}$ $=+6.00 \mathrm{~cm}$, and $h=2.00 \mathrm{~mm} .$ (Note that the vertical scale is different from the horizontal scale.)

Key Concepts

Object and Image Distances

These are the distances from the object to the lens (object distance) and from the lens to the image (image distance). They are critical inputs for the lens equation and directly affect the calculation of the image properties like location, size, and orientation in any optical system.

Multiple Lens Systems

In optical setups that include more than one lens, the intermediate image formed by one lens becomes the object for the next. This sequential relationship requires careful analysis using the lens equation for each lens in step, to accurately determine the final image position and size.

Sign Conventions in Optics

Proper use of the lens equation depends on understanding the sign conventions, which determine whether distances and focal lengths are positive or negative. Converging and diverging lenses are assigned different signs, and the object and image distances are treated according to their positions relative to the lens, ensuring consistent and accurate calculations.

Lens Equation

The lens equation, given by 1/f = 1/p + 1/q, relates the focal length of a lens to the distances of the object and the image from the lens. It is fundamental in determining where an image will form and what its properties will be, such as whether it is real or virtual.

Magnification

Magnification relates the height of the image to the height of the object and is calculated either as the ratio of image distance to object distance or directly through the sizes. It indicates whether the image is enlarged or reduced compared to the object and whether it is inverted or upright.

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