(II) A diverging lens with a focal length of -14 cm is placed 12 cm to the right of a converging

step 1 Emance distance will be given by inverse of the focal length minus inverse of the object distanc

(II) A diverging lens with a focal length of -14 cm is...

(II) A diverging lens with a focal length of $-14 \mathrm{cm}$ is placed 12 $\mathrm{cm}$ to the right of a converging lens with a focal length of $18 \mathrm{cm} .$ An object is placed 33 $\mathrm{cm}$ to the left of the converging lens. (a) Where will the final image be located? (b) Where will the image be if the diverging lens is 38 $\mathrm{cm}$ from the converging lens?

Key Concepts

Effect of Lens Separation

The separation between lenses in a compound optical system has a significant impact on the final image formation. Adjusting the distance between lenses changes the effective object distance for the following lens, which in turn affects the final image location. Understanding the role of lens spacing is essential for correctly analyzing and designing multi-lens setups.

Compound Lens Systems

In systems with multiple lenses, the image produced by the first lens typically acts as the object for a subsequent lens. This sequential process means that calculations must be done step-by-step, evaluating the image position from one lens and then using that position (and the appropriate separation distance) to determine the final image formed by the next lens.

Thin Lens Equation

The thin lens equation, 1/f = 1/do + 1/di, is a fundamental relationship in geometric optics that links the focal length (f) of a lens with the object distance (do) and the image distance (di). It is used to find the position of the image formed by a lens, whether it is converging or diverging, and serves as the basis for solving problems involving lens systems.

Sign Conventions in Geometrical Optics

Sign conventions are critical for correctly applying the thin lens formula. They help determine whether distances and focal lengths should be considered positive or negative, depending on factors such as the type of lens (converging vs. diverging), and whether the object or image is real or virtual. Proper use of these conventions ensures accurate calculation of image positions and characteristics.

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