(II) A plan convex lens (Fig. 2a) has one flat surface and...

(II) A plan convex lens (Fig. 2a) has one flat surface and the other has $R=15.3 \mathrm{cm} .$ This lens is used to view a red and yellow object which is 66.0 $\mathrm{cm}$ away from the lens. The index of refraction of the glass is 1.5106 for red light and 1.5266 for yellow light. What are the locations of the red and yellow images formed by the lens?

Key Concepts

Index of Refraction

The index of refraction is a property of a medium that measures how much the speed of light is reduced inside that medium compared to vacuum. It also dictates how much and in what way light bends when entering or exiting the material. In optics, different indices for various wavelengths cause variations in the focusing power of a lens.

Chromatic Aberration

Chromatic aberration is an optical phenomenon that occurs because the index of refraction of a lens material varies with wavelength. As a result, different colors (wavelengths) of light are focused at different distances from the lens, leading to images that do not converge perfectly. This effect must be accounted for in lens design when precise color imaging is required.

Thin Lens Equation

This equation relates the object distance, image distance, and focal length of a thin lens and is given by 1/f = 1/s_o + 1/s_i. It is a fundamental principle for determining where an image will form when an object is placed in front of a lens, assuming the lens has negligible thickness and light rays make small angles with the optical axis.

Lens Maker's Formula

This formula connects the focal length of a lens to its refractive index and the curvature of its surfaces. It is crucial for designing lenses and understanding how changes in the shape or material of a lens will affect its ability to focus light. For a lens with one flat side and one spherical side, the curvature of the spherical surface plays a significant role in determining the effective focal length.

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