(III) A planoconvex lens (Fig. 23-31a) has one flat surface...

(III) A planoconvex lens (Fig. 23$-$31a) has one flat surface and the other has $R =$14.5 cm. This lens is used to view a red and yellow object which is 66.0 cm away from the lens. The index of refraction of the glass is 1.5106 for red light and 1.5226 for yellow light. What are the locations of the red and yellow images formed by the lens? [$Hint$: See Section 23$-$10.]

Key Concepts

Planoconvex Lens

A planoconvex lens, having one flat surface and one convex (spherical) surface, is a basic type of converging lens commonly used in optics. Its behavior can be analyzed by applying formulas for refraction at curved surfaces, and it is often modeled using the thin lens approximation when its thickness is negligible compared to other distances. Its asymmetry (one flat and one curved surface) influences the way it focuses light and can have implications for minimizing aberrations.

Chromatic Aberration

Chromatic aberration arises from the dispersion of the refractive index, causing different wavelengths of light to focus at different points. This leads to images having colored fringes or a displacement between the images formed by different colors. Understanding chromatic aberration is essential for the design and analysis of optical systems that need to handle a range of wavelengths.

Refraction at a Spherical Surface

This concept describes how light bends when passing through a curved interface between two media with different refractive indices. It is governed by an equation involving object distance, image distance, refractive indices of the incident and transmitted media, and the radius of curvature, with careful attention needed for sign conventions. The formula allows us to predict the location of images formed by such curved surfaces.

Index of Refraction and Dispersion

The index of refraction indicates how much a light ray slows down in a medium compared to vacuum. Dispersion refers to the fact that the refractive index can vary with the wavelength (color) of light. This wavelength dependence is critical when analyzing how different colors are refracted differently, which directly affects image formation in lenses.

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