Physics - Spherical Lenses

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Introduction

  • A transparent material (normally glass) bound by two surfaces, of which one or both surfaces are spherical, is known as "spherical lens."

Lens

Convex Lens

  • A lens may have two spherical surfaces, bulging outwards (as shown in the image given below), is known as convex lens or a double convex lens.

Convex lens

  • The middle part of this lens is bulged (thicker) and at the both ends, it is narrow.

  • Convex lens converges the light rays; therefore, it is also known as converging lens.

Concave Lens

  • A lens may have two spherical surfaces, curved inwards (as shown in the image given below), is known as concave lens or a double concave lens.

Concave Lens

  • The middle part of this lens is narrow (curved inwards) and the both the edges are thicker.

  • Concave lens diverges the light rays; therefore, it is also known as diverging lens.

  • A lens, either a concave or a convex, has two spherical surfaces and each of these surfaces forms a part of the sphere. The centers of these spheres are known as centers of curvature, represented by English letter ‘C.’

  • As there are two centers of curvature, therefore, represented as ‘C1’ and ‘C2.’

  • An imaginary straight line, passing through both the centers of curvature of a lens, is known as principal axis.

  • Optical center is the central point of a lens. It is represented by ‘O.’

  • An aperture is the actual diameter of the circular outline of a spherical lens.

  • Principal focus of lens is represented by ‘F.’

  • A lens has usually two foci represented as F1 and F2.

  • Focal length is the distance between the principal focus and the optical center of a lens. It is represented by ‘f.’

  • The following table illustrates, the nature and position of images formed by a convex lens −

Position of Object Position of Image Size of Image Nature of Image Image
At infinity At the focus F2 Highly diminished, pointsized Real and inverted At infinity F2
Beyond 2F1 B/w F2 and 2F2 Diminished Real and inverted Beyond 2F1
At 2F1 At 2F2 Same size Real and inverted At 2F1
B/w F1 & 2F1 Beyond 2F2 Enlarged Real and inverted B/w F1 and 2F1
At focus F1 At infinity Infinitely large or highly enlarged Real & inverte d At F1
B/w focus F1 & optical center O On the same side of the lens as the object Enlarged Virtual and erect B/w F1

  • The following table illustrates, the nature and position of images formed by a concave lens −

Position of Object Position of Image Relative Size of Image Nature of Image Image
At infinity At the focus F1 Highly diminishe d, pointsized Virtual and erect At Focus1
B/w infinity & optical center O of the lens B/w F1 & optical center O Diminishe d Virtual and erect B/w O

Lens Formula

  • The formula is expressed as −

    • $$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$$

  • Lens formula expresses the relationships among the object-distance (i.e. u), image-distance (i.e. v), and focal length (i.e. f) of a lens.

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