The distance between an object and its image formed by a...

The distance between an object and its image formed by a diverging lens is $49.0 \mathrm{cm} .$ The focal length of the lens is $-233.0 \mathrm{cm} .$ Find (a) the image distance and (b) the object distance.

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Key Concepts

Lens Formula

The lens formula is a fundamental equation in geometric optics given by 1/f = 1/d_o + 1/d_i, which relates the focal length (f) of a lens to the object distance (d_o) and the image distance (d_i). This relationship is essential for analyzing and predicting how images are formed by lenses.

Sign Conventions

Sign conventions are critical in lens problems to correctly interpret the nature and location of images. For a diverging lens, the focal length is taken as negative, while the object distance is positive. The image distance also becomes negative, indicating that the image is virtual and located on the same side of the lens as the object.

Object and Image Distances

The object distance and image distance are key parameters in describing the geometry of image formation. Their relationship is determined by the lens formula, and understanding how to relate these distances allows one to compute the physical separation between the object and its image. This is particularly useful when additional information, such as the distance between the object and its image, is provided.

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