A diverging lens (f=-10.0 cm) is located 20.0 cm to the left of a converging lens (f=30.0 cm) .

step 1 So we have two lenses. We have lens L1 and then we have an L lens L2. The first lens L1 is a div

A diverging lens (f=-10.0 cm) is located 20.0 cm to the left...

A diverging lens $(f=-10.0 \mathrm{cm})$ is located $20.0 \mathrm{cm}$ to the left of a converging lens $(f=30.0 \mathrm{cm}) .$ A $3.00-\mathrm{cm}-$ tall object stands to the left of the diverging lens, exactly at its focal point. (a) Determine the distance of the final image relative to the converging lens. (b) What is the height of the final image (including the proper algebraic sign)?

A diverging lens $(f=-10.0 \mathrm{cm})$ is located $20.0 \mathrm{cm}$ to the left of a converging lens $(f=30.0 \mathrm{cm}) .$ A $3.00-\mathrm{cm}-$ tall object stands to the left of the diverging lens, exactly at its focal point.
(a) Determine the distance of the final image relative to the converging lens.
(b) What is the height of the final image (including the proper algebraic sign)?

Key Concepts

Sequential Lens Systems

In optical systems involving more than one lens, the image formed by the first lens serves as the object for the second lens. Understanding how to sequentially apply the thin lens equation and magnification for each lens is critical to determine the final image properties, such as its position and size relative to the system components.

Magnification

Magnification describes the ratio of the height of the image to the height of the object and is directly related to the distances from the lens via the relationship m = -d_i/d_o. It provides information on whether the image is enlarged or diminished, and it also indicates if the image is inverted or upright, which is important in multi-lens systems.

Sign Conventions in Optics

Sign conventions are fundamental in lens calculations to correctly designate object distances, image distances, and focal lengths. They ensure that the calculations reflect the correct geometry of the situation, distinguishing between real and virtual images, and between converging and diverging behaviors of lenses.

Thin Lens Equation

The thin lens equation (1/f = 1/d_o + 1/d_i) establishes the relationship between the focal length of a lens and the distances of the object (d_o) and the image (d_i) from the lens. This formula is crucial for calculating where an image will form given a specific lens and object placement, and it is applicable to both converging and diverging lenses with appropriate sign conventions.

Focal Length

Focal length is a key property of a lens that indicates the distance from the lens at which parallel rays of light converge (for converging lenses) or appear to diverge (for diverging lenses). It is not only essential for determining image distances using the thin lens equation but also affects the magnification and overall behavior of the lens in optical setups.

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