In terms of a light ray, optics describes how light travels. In geometrical optics, a light ray is used to create approximations of models for light propagation. At the point where two different media meet and the refractive index changes, light rays tend to bend. The laws governing how light moves via optical devices are provided by geometric optics.
Geometrical optics could explain geometric imaging and aberrations. The lens is one of these axially symmetric optical devices that permits and refracts light rays to either converge or diverge.
History of Optics
Indians, Egyptians, Greeks, and Romans all had notions about optics in the prehistoric era. They also produced lenses. The Arabians and the English were innovators in the development of theories about the speed of light and its research during the Middle Ages.
Huygens and Newton both established their own theories on the nature of light and its behaviour during the 16th and 17th centuries, which helped the field advance. In the end, debunking erroneous notions about the existence of the ether and other things was greatly helped by the study of light and the determination of its speed. The study of optics can be credited with giving rise to quantum physics.
Important Optics Formula
Optometry is a crucial field where the power of lenses is used.
Conditions for total internal reflection:
The angle of incidence must be greater than the critical angle, the light must be travelling from a more dense medium into a less dense medium (i.e. glass to air), and the light must be travelling at a constant speed.
Refraction at a spherical refracting surface
The fundamental principle underlying the design and operation of lenses is refraction at spherical surfaces. Refraction is the bending of a light wave as it passes through a transparent medium. This phenomenon is caused by a change in the incident light wave’s speed.
Rarer to a denser medium
The speed of light is faster in rarer media than in denser media. As a result, when light travels from a denser medium to a rarer medium, it deviates from the norm and light tends to move towards normal as it travels from rarer to denser medium.
Denser to rarer medium
When light travels from a denser to a rarer medium, its speed increases, causing it to deviate from its usual path. Light, therefore, travels more quickly as it transitions from a denser to a rarer medium.
Lens Maker’s Formula
1/f = (μ – 1)(1/R1 – 1/R2)
where is the lens’s material’s refractive index
The curvature radii of the lens’s two surfaces are R1 and R2.
Formula for a lens: 1/v – 1/u = 1/f
Magnification in linear form: m = hi/ho = v/u
Lens power: P = 1/f if f is measured in meters. Dioptre D
Combination of two thin lenses
Compound lenses are a particular type of lens that consists of two thin lenses mounted on a common axis, typically closer to one another or frequently cemented together.
Lenses in contact
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Lenses separated by a finite distance
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m = 1 + D/f, where D is the minimum distance needed to see clearly, or 2.5 cm
The ratio of the final image’s angle at the eye to the object’s angle at the eye when both the final image and the object are close enough to each other to be clearly seen.
Resolving power of a microscope
Power of resolution =1/d = (2μSinθ)/λ
where the medium’s refractive index is
The light’s wavelength is λ
The angle of the light cone from the point object to the objective lens is half θ
Resolving power of a telescope
Resolving power = 1/dθ = D/1.22λ
where D is the object lens’s diameter.
The light’s wavelength is
Laws of reflection
The angle I = (r)
The normal at the point of incidence, the reflected ray, and the incident ray all lie in the same plane.
The mirror formula’s equation is 1f=1v+1u. The reflecting part of the concave spherical mirror caves inwards, while the reflecting part of the convex spherical mirror caves outwards. In a convex mirror, the focal length f is positive and the object distance u is negative.
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