Marking Scheme

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Solutions for 18.2

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Interference

Interference is the addition (superposition) of two or more waves that results in a new wave pattern. Interference usually refers to the interaction of waves that are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same frequency.














The principle of superposition of waves states that the resultant displacement at a point is equal to the vector sum of the displacements of different waves at that point. If a crest of a wave meets a crest of another wave at the same point then the crests interfere constructively and the resultant wave amplitude is greater. If a crest of a wave meets a trough of another wave then they interfere destructively, and the overall amplitude is decreased.

Optical path length

optical path length (OPL) is the product of the geometric length of the path light follows through the system, and the index of refraction of the medium through which it propagates

 A difference in optical path length between two paths is often called the optical path difference (OPD)


The refractive index, n, of a medium is defined as the ratio of the velocity, c, of a wave phenomenon such as light or sound in a reference medium to the phase velocity, v_p in the medium itself:

Lenses are classified by the curvature of the two optical surfaces. A lens is biconvex (or double convex, or just convex) if both surfaces are convex. If both surfaces have the same radius of curvature, the lens is equiconvex. A lens with two concave surfaces is biconcave (or just concave). If one of the surfaces is flat, the lens is plano-convex or plano-concave depending on the curvature of the other surface. A lens with one convex and one concave side is convex-concave or meniscus. It is this type of lens that is most commonly used in corrective lenses.

Solution for module lower and upper 6

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module for lower and upper 6 download here

A light ray is a line or curve that is perpendicular to the light's wavefronts (and is therefore collinear with thewave vector).

A slightly more rigorous definition of a light ray follows from Fermat's principle, which states that the path taken between two points by a ray of light is the path that can be traversed in the least time.

Geometrical optics is often simplified by making the paraxial approximation, or "small angle approximation." The mathematical behavior then becomes linear, allowing optical components and systems to be described by simple matrices. This leads to the techniques of Gaussian optics and paraxial ray tracing, which are used to find basic properties of optical systems, such as approximate image and object positions andmagnifications.

Refraction occurs when light travels through an area of space that has a changing index of refraction. The simplest case of refraction occurs when there is an interface between a uniform medium with index of refraction n₁ and another medium with index of refraction n₂. In such situations, Snell's Law describes the resulting deflection of the light ray:

where θ₁ and θ₂ are the angles between the normal (to the interface) and the incident and refracted waves, respectively. This phenomenon is also associated with a changing speed of light as seen from the definition of index of refraction provided above which implies:

Total internal reflection is an optical phenomenon that occurs when a ray of light strikes a medium boundary at an angle larger than the critical angle with respect to the normal to the surface. If the refractive index is lower on the other side of the boundary, no light can pass through and all of the light is reflected. The critical angle is the angle of incidence above which the total internal reflection occurs.

When light crosses a boundary between materials with different refractive indices, the light beam will be partially refracted at the boundary surface, and partially reflected. However, if the angle of incidence is greater (i.e. the ray is closer to being parallel to the boundary) than the critical angle — the angle of incidence at which light is refracted such that it travels along the boundary — then the light will stop crossing the boundary altogether and instead be totally reflected back internally. This can only occur where light travels from a medium with a higherrefractive index to one with a lower refractive index. For example, it will occur when passing from glass to air, but not when passing from air to glass.

Electromagnetic waves were first postulated by James Clerk Maxwell and subsequently confirmed by Heinrich Hertz. Maxwell derived a wave form of the electric and magnetic equations, revealing the wave-like nature of electric and magnetic fields, and their symmetry. Because the speed of EM waves predicted by the wave equation coincided with the measured speed of light, Maxwell concluded that light itself is an EM wave.

According to Maxwell's equations, a time-varying electric field generates a magnetic field and vice versa. Therefore, as an oscillating electric field generates an oscillating magnetic field, the magnetic field in turn generates an oscillating electric field, and so on. These oscillating fields together form an electromagnetic wave.

A quantum theory of the interaction between electromagnetic radiation and matter such as electrons is described by the theory of quantum electrodynamics.