1.6 is a refractive index of plano-convex lens, then the...

$1.6$ is a refractive index of plano-convex lens, then the radius of curvature of the curved surface is $60 \mathrm{~cm}$. The focal length of the lens is $\mathrm{cm}$
(B) $10 \overline{0}$
(A) 50
(C) $-50$
(D) $-100$

Key Concepts

Sign Conventions in Optics

Sign conventions in optics determine the positive or negative values assigned to the focal length, radius of curvature, and image distances. These conventions help maintain consistency in calculations and predictions of image properties depending on whether the surfaces are convex or concave and whether the lens is converging or diverging.

Lens Maker's Formula

The Lens Maker's Formula relates the focal length of a lens to the refractive index of the lens material and the radii of curvature of its surfaces. For lenses where one surface is flat, the formula simplifies and directly links the focal length with the refractive index and the radius of curvature of the curved surface.

Focal Length

The focal length of a lens is the distance from the lens at which parallel rays of light converge to a focus (for converging lenses) or appear to diverge from (for diverging lenses). It is a fundamental property that dictates the magnifying and image-forming characteristics of the lens.

Plano-Convex Lens

A plano-convex lens is an optical lens with one flat (plano) surface and one outwardly curved (convex) surface. This type of lens is used to focus light and its behavior is analyzed by considering the contribution of its curved surface while the flat side does not contribute to curvature-based refraction.

Refractive Index

The refractive index of a material quantifies how much the speed of light is reduced inside that material compared to vacuum. It is an essential property in optics as it determines how much a light ray will bend or refract when entering or exiting a medium.

Radius of Curvature

The radius of curvature is the radius of the spherical surface that forms the curved part of a lens. It is a critical parameter in determining how strongly a lens will converge or diverge light rays, as the curvature directly influences the lens's focal properties.

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