An object 2.00 cm high is placed 40.0 cm to the left of a converging lens having a focal length

step 1 Here we will have Q1 equals 1 over f minus 1 over p1 inverse equals 1 over 30 minus 1 over 40 in

An object 2.00 cm high is placed 40.0 cm to the left of a...

An object 2.00 $\mathrm{cm}$ high is placed 40.0 $\mathrm{cm}$ to the left of a converging lens having a focal length of $30.0 \mathrm{cm} .$ A diverging lens with a focal length of $-20.0 \mathrm{cm}$ is placed 110 $\mathrm{cm}$ to the right of the converging lens. (a) Determine the position and magnification of the final image. (b) Is the image upright or inverted? (c) What If? Repeat parts (a) and (b) for the case in which the second lens is a con- verging lens having a focal length of $+20.0 \mathrm{cm} .$

Key Concepts

Compound Lens Systems

In a compound lens system, where light passes sequentially through multiple lenses, the image formed by the first lens serves as the object for the next lens. Analyzing such systems requires applying the thin lens equation and magnification formula consecutively while carefully tracking the distances between lenses and using the proper sign conventions. This approach enables the calculation of the final image position, size, and orientation.

Magnification

Magnification quantifies the size relationship between the image and the object, defined as m = h_i/h_o and also given by m = -d_i/d_o for a single lens. It indicates not only the size of the image but also its orientation (upright or inverted). Understanding magnification is essential for analyzing the scale of image formation in optical systems.

Thin Lens Equation

The thin lens equation (1/f = 1/d_o + 1/d_i) relates the focal length of a lens to the distances of the object (d_o) and image (d_i). It is a fundamental principle used to determine the position at which an image is formed by a lens, whether the image is real or virtual, and how far it is from the lens.

Sign Conventions

Sign conventions are critical in optics for determining the correct signs for object and image distances as well as for focal lengths. These conventions dictate that distances are measured from the optical center of the lens, with directions (positive and negative) assigned based on the orientation of the light. Correct use of sign conventions ensures accurate calculations of image properties such as location and magnification.

Image Formation

Image formation involves understanding how light rays converge or diverge to create an image. Converging (convex) lenses typically form real images when the object is located outside the focal point, while diverging (concave) lenses form virtual images. This concept is vital to predicting whether the final image will be upright or inverted and determining its characteristics.

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