Two lenses that are 35 cm apart are used to form an image, as shown in FlGURE 26-71 . Lens 1 is

step 1 In this question, we are given this lens setup. Lens 1 is diverging lens with focal length minus

Two lenses that are 35 cm apart are used to form an image,...

Two lenses that are 35 $\mathrm{cm}$ apart are used to form an image, as shown in FlGURE $26-71 .$ Lens 1 is diverging and has a focal length $f_{1}=-7.0 \mathrm{cm} ;$ lens 2 is converging and has a focal length $f_{2}=14 \mathrm{cm} .$ The object is placed 24 $\mathrm{cm}$ to the left of lens $1 .$ (a) Use a ray diagram to find the approximate location of the image. (b) Is the image upright or inverted? (c) Is the image real or virtual? Explain.

Two lenses that are 35 $\mathrm{cm}$ apart are used to form an image, as shown in FlGURE $26-71 .$ Lens 1 is diverging and has a focal
length $f_{1}=-7.0 \mathrm{cm} ;$ lens 2 is converging and has a focal length $f_{2}=14 \mathrm{cm} .$ The object is placed 24 $\mathrm{cm}$ to the left of lens $1 .$ (a) Use a
ray diagram to find the approximate location of the image. (b) Is the
image upright or inverted? (c) Is the image real or virtual? Explain.

Key Concepts

Thin Lens Equation

This is the fundamental relationship in geometric optics that relates the object distance, image distance, and the focal length of a lens through the formula 1/f = 1/do + 1/di. The equation is essential for determining where an image will form by a single lens and involves careful use of sign conventions to differentiate between real and virtual images.

Sign Conventions

In optics, proper sign conventions are crucial for correctly applying formulas like the thin lens equation. They determine the positive or negative nature of the object distance, image distance, and focal length depending on the lens type (converging or diverging) and the orientation of the object relative to the lens.

Ray Diagram Construction

Ray diagrams provide a visual method to trace the paths of light rays through one or more lenses to locate the image. This technique involves drawing key rays, such as those that pass through the center of a lens or focus at the focal points, to understand the path of the light and ascertain the position, orientation, and nature of the final image.

Converging and Diverging Lens Behavior

Converging lenses, which have positive focal lengths, tend to bring light rays together to form real images, whereas diverging lenses, with negative focal lengths, spread light rays apart and typically form virtual images. Understanding these intrinsic behaviors is essential when analyzing optical systems involving both types of lenses.

Compound Lens Systems

When multiple lenses are placed in sequence, the image formed by the first lens serves as the object for the second lens. Analyzing such systems requires sequential application of the thin lens equation and ray diagrams, taking into account the separation between the lenses to determine the final image characteristics.

Real and Virtual Images

Real images are formed when light rays actually converge at a point, and they can be projected onto a screen, while virtual images occur where rays appear to diverge from a common point but do not actually converge. This distinction helps determine not only where the image is located but also its orientation and whether it is accessible for further manipulation in optical setups.

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