A converging lens with a focal length of 15.0 cm and a diverging lens are placed 25.0 cm apart

step 1 So for the first length we have 1 over p1 plus 1 over q1 equals 1 over f1 now p1 equals 22 centi

A converging lens with a focal length of 15.0 cm and a...

A converging lens with a focal length of $15.0 \mathrm{~cm}$ and a diverging lens are placed $25.0 \mathrm{~cm}$ apart, with the converging lens on the left. A $2.00-\mathrm{cm}$ -high object is placed $22.0 \mathrm{~cm}$ to the left of the converging lens. The final image is $34.0 \mathrm{~cm}$ to the left of the converging lens. (a) What is the focal length of the diverging lens? (b) What is the height of the final image? (c) Is the final image upright or inverted?

A converging lens with a focal length of $15.0 \mathrm{~cm}$ and a diverging lens are placed $25.0 \mathrm{~cm}$ apart, with the converging lens on the left. A $2.00-\mathrm{cm}$ -high object is placed $22.0 \mathrm{~cm}$ to the left of the converging lens. The final image is $34.0 \mathrm{~cm}$ to the left of the converging lens.
(a) What is the focal length of the diverging lens?
(b) What is the height of the final image? (c) Is the final image upright or inverted?

Key Concepts

Lens Formula

The lens formula, given by 1/f = 1/d_o + 1/d_i, is a fundamental concept in geometric optics that relates the object distance (d_o), image distance (d_i), and the focal length (f) of a lens. This equation allows one to compute the unknown parameter if the other two are known, and it is essential for analyzing image formation by single lenses.

Sign Conventions in Optics

Accurate analysis of optical systems requires strict adherence to sign conventions. These conventions determine the positive or negative values for object distances, image distances, and focal lengths. For instance, in the lens equation, real images and objects are typically assigned positive distances, while virtual images or diverging lens focal lengths are often given negative values. Understanding these rules is crucial for solving problems correctly.

Magnification

Magnification in optics relates the height of the image to that of the object and is given by the ratio m = h_i/h_o = -d_i/d_o. This concept not only indicates how much larger or smaller the image is compared to the object but also signifies whether the image is upright (m positive) or inverted (m negative), playing an essential role in interpreting the final image characteristics.

Multiple-Lens Systems

In optical setups involving more than one lens, such as a system with a converging and a diverging lens, the image formed by the first lens becomes the object for the second. Analyzing such systems involves applying the lens formula sequentially and understanding how distances between lenses affect the overall image formation. This concept is critical for solving problems that involve composite optical systems.

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