A double-convex lens with equal 28.5-cm curvature radii is made from glass with refractive indic

step 1 In this particular case, we will have 1 over S plus 1 over S prime equals 1 over F equals N minu

A double-convex lens with equal 28.5-cm curvature radii is...

A double-convex lens with equal $28.5-\mathrm{cm}$ curvature radii is made from glass with refractive indices $n_{\text {red }}=1.512$ and $n_{\text {violet }}=1.547$. If a point source of white light is located on the lens axis at $75.0 \mathrm{~cm}$ from the lens, over what distance will its visible image be smeared?

Key Concepts

Double-convex Lens

A double-convex lens is a type of converging lens that is curved outward on both sides. Its design allows it to converge parallel incoming light rays to a focal point on the lens’s optical axis, making it useful in focusing applications such as imaging systems, magnifiers, and corrective lenses.

Lensmaker's Formula

The Lensmaker's Formula relates the focal length of a lens to the radii of curvature of its surfaces, the refractive index of the lens material, and the lens thickness (when considered in the thin lens approximation, the thickness is often neglected). This formula is crucial for designing lenses with desired focal properties and understanding how changes in geometry or material affect image formation.

Chromatic Aberration

Chromatic aberration is an optical phenomenon where a lens fails to focus all colors to the same convergence point because the refractive index of the material varies with wavelength. This variation leads to different focal lengths for different colors, resulting in a color-dependent blur or smear in the image, which is a common problem in optical instruments that use simple lens systems.

Dispersion

Dispersion refers to the dependence of a material's refractive index on the wavelength of light. This property causes different colors to refract at slightly different angles when passing through a lens, which is the underlying physical reason for chromatic aberration. Understanding dispersion is essential for developing corrective measures, such as using compound lenses or specialized coatings, to minimize color fringes in optical systems.

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