An object of height 3 cm is placed at a distance of 25 cm in front of a converging lens of focal

step 1 Here we are trying to find the image distance GI equals 1 over f minus 1 over DO Inverse of that

An object of height 3 cm is placed at a distance of 25 cm in...

An object of height 3 cm is placed at a distance of 25 $\mathrm{cm}$ in front of a converging lens of focal length $20 \mathrm{cm},$ to be referred to as the first lens. Behind the lens there is another converging lens of focal length $20 \mathrm{cm}$ placed $10 \mathrm{cm}$ from the first lens. There is a concave mirror of focal length 15 $\mathrm{cm}$ placed $50 \mathrm{cm}$ from the second lens. Find the location, orientation, and size of the final image.

Key Concepts

Compound Optical Systems

In systems with multiple optical elements, such as several lenses or mirrors in sequence, the image produced by one element often serves as the object for the next. Analyzing each stage separately using the thin lens or mirror equation allows one to track the position, orientation, and magnification of the final image.

Thin Lens Equation

This fundamental formula, 1/f = 1/do + 1/di, relates the focal length (f) of a thin lens to the distances of the object (do) and the image (di) from the lens. It is essential for determining where an image is formed by a single lens, and forms the basis for understanding more complex optical systems.

Sign Conventions in Optics

Correct application of sign conventions is crucial in optics to indicate the direction of distances and to distinguish between real and virtual images. Distances measured in the direction of incident light are typically taken as positive, while others are negative, and the conventions also determine the orientation (upright or inverted) of the images.

Magnification

Magnification describes the ratio of the image size to the object size and is given by m = -di/do for a lens. It also indicates the orientation of the image, with a negative magnification corresponding to an inverted image. This concept is important for determining the size and orientation in each step of a compound system.

Mirror Equation

For curved mirrors, particularly spherical mirrors, a similar equation is used: 1/f = 1/do + 1/di. Understanding image formation by mirrors, including the differences in sign conventions compared to lenses, is essential when analyzing systems that combine both lenses and mirrors.

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