Two lenses, separated by a distance of 21.0 cm, are used in combination. The first lens has a f

step 1 We have object distance equals 1 over f1 minus 1 over p1 inverse equals 1 over 30 minus 1 over 1

Two lenses, separated by a distance of 21.0 cm, are used in...

Two lenses, separated by a distance of $21.0 \mathrm{~cm}$, are used in combination. The first lens has a focal length of $+30.0 \mathrm{~cm} ;$ the second has a focal length of $-15.0 \mathrm{~cm}$. An object, $2.0 \mathrm{~mm}$ long, is placed $1.8 \mathrm{~cm}$ before the first lens. (a) What are the intermediate and final image distances relative to the corresponding lenses? (b) What is the total magnification? (c) What is the height of the final image?

Two lenses, separated by a distance of $21.0 \mathrm{~cm}$, are used in combination. The first lens has a focal length of $+30.0 \mathrm{~cm} ;$ the second has a focal length of $-15.0 \mathrm{~cm}$. An object, $2.0 \mathrm{~mm}$ long, is placed $1.8 \mathrm{~cm}$ before the first lens. (a) What are the intermediate and final image distances relative to the corresponding lenses?
(b) What is the total magnification? (c) What is the height of the final image?

Key Concepts

Sequential Image Formation

The concept of sequential image formation involves calculating the image from the first optical element and then treating that image as the object for the next element in the system. This step-by-step approach is essential in analyzing systems of multiple lenses, enabling the determination of intermediate image distances, final image distance, and overall magnification.

Sign Conventions

Correctly applying sign conventions is critical in optical calculations. These conventions assign positive or negative values to object distances, image distances, and focal lengths based on the lens type and the nature of the image (real or virtual). Adhering to these rules ensures accurate determination of image positions and magnifications in multi-lens systems.

Thin Lens Equation

The thin lens equation (1/f = 1/do + 1/di) is fundamental in geometrical optics. It relates the object distance (do), the image distance (di), and the focal length (f) of a lens. This formula is used to determine the position of the image formed by a single lens, and it forms the basis for subsequent calculations in multi-lens systems.

Magnification

Magnification in optics quantifies how much larger or smaller the image is relative to the object. For a thin lens, the magnification is given by m = -di/do, where the negative sign indicates orientation (inversion for real images). In a multi-lens setup, the overall magnification is the product of the magnifications of the individual lenses, providing insight into the final image size.

Compound Lens System

A compound lens system consists of two or more lenses in combination, where the image produced by one lens serves as the object for the next. This sequential imaging process requires careful application of the lens formula for each lens, accounting for separations and sign conventions, to determine the final image properties.

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