4. Lenses
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A lens is a piece of transparent refracting material (usually glass) bound by two surfaces, at least one of which is curved (spherical). Lenses refract light and are the key components of eyeglasses, cameras, microscopes, and telescopes.
4.1 Types of Lenses
Convex (converging) lens: Thicker at the middle than at the edges. It converges (brings together) a parallel beam of light to a single point after refraction, called the principal focus. Convex lenses are also called converging lenses and can form both real and virtual images.
Concave (diverging) lens: Thinner at the middle than at the edges. It diverges (spreads out) a parallel beam of light after refraction, so that the rays appear to come from a single point (the focus) on the same side as the incident light. Concave lenses always form a virtual, erect, and diminished image, no matter where the object is placed.
4.2 Image Formation by a Convex Lens
Position of Object | Position of Image | Nature of Image |
|---|---|---|
At infinity | At focus F₂ (on the other side) | Real, inverted, highly diminished |
Beyond 2F₁ | Between F₂ and 2F₂ | Real, inverted, diminished |
At 2F₁ (twice the focal length) | At 2F₂ | Real, inverted, same size |
Between F₁ and 2F₁ | Beyond 2F₂ | Real, inverted, magnified |
At focus F₁ | At infinity | Real, inverted, highly magnified |
Between optical centre and F₁ | Same side as object | Virtual, erect, magnified |
The last case, where the object is placed between the optical centre and the focus of a convex lens, produces a virtual, erect, and magnified image and is the operating principle of the simple magnifying glass. In every other position, the convex lens produces a real, inverted image, which is why it is used in cameras and projectors.
4.3 Lens Formula and Magnification
The lens formula relates the object distance (u), image distance (v), and focal length (f) of a thin lens:
1/v − 1/u = 1/f
Linear magnification for a lens is given by:
m = height of image / height of object = v/u
By the standard sign convention, the focal length of a convex lens is taken as positive, while the focal length of a concave lens is taken as negative.
Image formation by a concave lens
Unlike a convex lens, a concave lens forms only one kind of image regardless of where the object is placed: the image is always virtual, erect, and diminished, and it always forms on the same side of the lens as the object, between the optical centre and the focus. As the object is moved farther from the lens, the image likewise moves farther away (up to the focus) while remaining virtual and erect — this behaviour parallels that of a convex mirror among spherical mirrors, and both devices (concave lens and convex mirror) are used precisely where a smaller, non-magnified, always-erect view is wanted, such as in the concave spectacle lenses used to correct myopia, or the wide-view mirrors used in vehicles.
A note on lens aberrations
Real lenses do not form perfectly sharp images in every situation, due to two well-known optical defects. Chromatic aberration occurs because a lens refracts different colours (wavelengths) of light by slightly different amounts, exactly as a prism does, so that a single lens brings different colours to a focus at slightly different points, producing coloured fringes around the image; this is usually minimised by combining a convex and a concave lens made of different types of glass into an 'achromatic doublet'. Spherical aberration occurs because rays striking near the edge of a spherical lens (or mirror) are focused at a slightly different point than rays passing near the centre, blurring the image; this can be reduced by using only the central part of the lens (stopping down the aperture) or by using specially shaped (aspherical) lens surfaces. Awareness of these two terms — chromatic aberration and spherical aberration — is occasionally tested directly as definitional questions.
4.4 Power of a Lens
The power of a lens is a measure of how strongly it converges or diverges light rays falling on it, and is defined as the reciprocal of its focal length (measured in metres):
P = 1/f (f in metres)
The SI unit of power of a lens is the dioptre, denoted D. One dioptre is the power of a lens whose focal length is exactly 1 metre. A convex (converging) lens has positive power, while a concave (diverging) lens has negative power. Opticians prescribe spectacle lens power in dioptres — this is one of the most commonly asked numerical/factual points in SSC-type exams (unit of power of a lens = dioptre).
4.5 Combination of Lenses
When two or more thin lenses are placed in close contact along the same axis, the power of the combination is simply the algebraic sum of the individual powers:
P = P₁ + P₂ + P₃ + …
and correspondingly, 1/f = 1/f₁ + 1/f₂ + 1/f₃ + … This principle is used by opticians and in the design of compound optical instruments (microscopes, telescopes, cameras with multiple lens elements) to correct for defects such as chromatic and spherical aberration, and to achieve a desired overall power or magnification that a single lens could not easily provide.
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