#### Geometric and Wave optics, Physics tutorial

Introduction:

Optics is a foundation stone of photonics systems and applications. Geometrical optics, or ray optics, is to learn geometry of paths of lights and imagery through optical systems. Light will be treated as the form of energy that travels in straight lines known as rays. When light comes to be considered as waves, it will be observed that shadows cast by objects are not as sharp as rectili near propagation suggests because of diffraction and interference effects of wave. Therefore, there is a simple supposition for geometrical optics, which is rays of light propagate along straight lines until they get reflected, refracted, or absorbed at the surface.

When the size of the physical and optical objects of the system are much larger than wavelength of the light (or as λ→ 0 ), we all are in realm of geometrical optics.

Geometrical optics, or ray optics, explains light propagation in terms of rays. Ray in geometric optics is the abstraction, or instrument, helpful in evaluating paths along which light propagates in certain classes of situations.

Simplifying assumptions of geometrical optics comprise that light rays:

• propagate in rectilinear paths as they travel in the homogeneous medium
• bend, and in particular circumstances may split in two, at interface between two different media
• follow curved paths in the medium in which refractive index changes
• May be absorbed or reflected.

Geometrical optics doesn't account for certain optical effects like diffraction and interference. This simplification is helpful in practice; it is the excellent approximation when wavelength is small compared to size of structures with which light interacts. Methods are mainly helpful in explaining geometrical features of imaging, comprising optical aberrations. When the ray of light hits boundary between two transparent materials, it is divided in reflected and a refracted ray.

Law of reflection: It says that reflected ray lies in plane of incidence, and angle of reflection equals angle of incidence.

Law of refraction: It says that refracted ray lies in plane of incidence, and sine of the angle of refraction divided by sine of the angle of incidence is the constant.

Sin Θ1/sin Θ2 = n

Where n is the constant for any two materials and given color of light. It is called as refractive index.

Limitations of Geometrical Optics

• Optical system can't collect all parts of spherical wavefront diffraction
• Geometrical optics neglects diffraction effects
• Geometrical optics λ → 0
• Physical optics λ → 0
• Simplicity of geometrical optics generally outweighs limitations

Plane mirrors:

Light rays are coming from the source and reflecting off each point of object in all directions. Rays spread upon leaving object, and then each ray reflects from mirror according to law of reflection. Eye extends back diverging reflected rays to see the image behind mirror. The image produced in this way by extending back reflected diverging rays is known as virtual image. Virtual image can't be projected on the screen. Light doesn't physically come together, but rather, eye (or camera) interprets diverging rays as originating from the image behind mirror. Because of law of reflection, image formed by the plane mirror is same distance behind mirror as the object is in front of the mirror.

Brewster's angle:

Light reflected from surface of the material is partially polarized. The ray incident on transparent surface at a certain angle will be partly refracted and partly reflected in the plane polarized ray. This angle of maximum plane polarization is known as Brewster's angle, named after Sir David Brewster. Equation is tan θ = n, where n is index of refraction of reflecting surface.

Total internal reflection:

When light travels from the material with the higher n to one with the lower n, at certain angles all of the light is reflected. This effect is known as total internal reflection.

Optical lenses:

The optical lens functions by refracting light at its interfaces. The lens will be supposed to be thin, in which case thickness of lens is negligible compared with it focal length. Lenses are basically of two kinds. The converging lens causes parallel rays to converge, and diverging lens causes parallel rays to diverge. Definitions for optical axis, focal point, and focal length given for curved mirrors hold true for lenses, with addition that lenses have focal points on each side of lens.

Dispersion:

Velocity of light in the material, and therefore index of refraction of material, depends on wavelength of the light.  As refractive index depends on wavelength of the light, light waves with different wavelengths and thus different colors are refracted through different angles.  This is known as dispersion, as white light is dispersed into its component colors while traveling through material.

Wave Optics:

One of the weird things about light is that some of properties can be described only by treating it as wave, whereas others can be described only by treating it as particle. Classical physics which we have applied until now handles only particle properties of light. Some phenomena that can only be explained with a wave model of light.

Branch of physics handling the study of optical phenomena is known as optics. This can be divided in two categories, ray optics and wave optics. Wave optics explains connection between waves and rays of light. Wave theory of light was put forward by Huygens and later customized by Fresnel. There are different phenomena related to wave nature of light.

Diffraction:

Diffraction is a bending of light around obstacles: it causes interference patterns like in Young's double-slit experiment. The diffraction grating is the screen with the bunch of parallel slits, each spaced distance d apart. Analysis is exactly the same as in double-slit case: there are still maxima at d sin Θ = n λ and minima at d sin Θ λ = (n + 1/2) λ. The only difference is that pattern doesn't fade out as quickly on sides.

Young's Double-Slit Experiment:

Double-slit experiment involves light being shone on thescreen with two very narrow slits in it, separated by the distance d. Second screen is set up thedistance L from first screen, on which light passing through two slits shines. Assume we have coherent light-i.e., light of thesingle wavelength, which is all traveling in phase. This light hits first screen with two parallel narrow slits, both of which are narrower than. As slits are narrower than wavelength, the light spreads out and distributes itself across far screen.

Polarization:

Light is the transverse wave, signifying that it oscillates in the direction perpendicular to direction in which it is traveling. Though, the wave is free to oscillate right and left or up and down or at any angle between vertical and horizontal.

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