Light and Optics Flashcards
General properties of light are its ________ and its ______ such that the angle of ______ (as measured with respect to the surface normal) is _______________________________.
- rectilinear propagation
- reflection
- reflection
- equal in magnitude to its angle of incidence.
Refraction of light is governed by _______, ____________, with θi,t and ni,t, respectively, the angle of incidence (i) / transmission (t) and the index of refraction of the medium of incidence (i) / transmission (t).
- Snell’s law
- ni sin θi = nt sin θt
• The propagation of light follows _________, which states that _____________________________________________.
- Fermat’s theorem
- the actual path between two points taken by a beam of light is the one which is transversed in the least time
It can also be described according to ___________, in that ________________________________________________________.
- Huygens’s principle
- every point on a wavefront acts as a source of a new wavefront propagating radially outwards
Optical path length is defined as___________________________________________. As a consequence, the speed of light in such a medium is given by ___.
- the distance that light travels in a vacuum in the same time that it travels a distance d in a medium with index of refraction n
- c/n
Total internal reflection occurs when _____________________________________ . This is the case for transmission from an optically denser (larger n) to an optical less dense (smaller n) medium for angles of incidence larger than the critical angle θc =_______.
- the angle of incidence is so large that the angle of transmission, by virtue of Snell’s law, would become larger than 90o
- sin−1 (nt/ni)
Light paths are reversible. That is, _________________________________________________________.
- the path of light from A to B will be identical to the (reverse) path from B to A
Light can be described as a wave ψ = Ae i(k·r−ωt) . By ignoring polarisation and considering only one-dimensional propagation along the positive x direction, this can be simplified to ψ = ________.
- Aei(kx−ωt)
In general, the intensity of light for a given polarisation direction is proportional to _________, where the asterisk * refers to the __________.
- |ψ|2 = ψ ∗ψ
- complex conjugate
For light propagating in a medium of index of refraction n, we need to substitute c → c/n, hence λ = c/f → (c/n)/f = λ/n and k = 2π/λ → kn. As a consequence, the position-dependent part of the phase becomes knx, which is equivalent to the usual expression for the wave with x → nx, i.e., what matters is the optical path nx.
In Young’s double slit experiment, _______________________________________________, resulting in an______________ on a detection screen at a distance L. For any point on the screen, the light can interfere _______________ or ____________, depending on the _____________________ to that point.
- monochromatic light passes through two narrow slits with separation d
- interference pattern
- destructively or constructively
- difference in optical path from each of the slits
Two light rays will interfere destructively if their path difference is_______. This corresponds to a phase difference at a particular point of _______, with m integer. Similarly, they will interfere constructively if their path difference is __, i.e., their phase difference at a particular point is m 2π.
- (m+ 1/2 )λ
- (m+ 1/2 )2π
- mλ
In the Fraunhofer limit, _____________________________________________, in which case the relevant optical path difference is given by_____, where θ is the angle of detection.
- the light rays from the two slits are presumed to propagate (approximately) parallel to a point on the screen
- d sin θ
We can write ψ1 = E e(ikr1 − iωt) and ψ2 = E e(ikr1 + iδ − iωt) for the light waves originating from the two slits, where δ = ______. We can calculate the light intensity at a particular point I ∝ ψ∗ψ by noting that the total ψ = A e−iωt = (E eikr1 + E eikr1+iδ) e−iωt, hence I ∝ A∗
- kd sin θ
Generally, we determine an interference (or diffraction) pattern by __________________________, to yield the resulting complex __________. In the example of the Young’s double slit experiment, we find A = _________________, with δ = ______, and I ∝ ____________________.
- summing waves in complex exponential notation
- amplitude A
- A = 2E eikr1+iδ/2 cos (δ/2)
- kd sin θ
- 4E2 cos2(πd sinθ/ λ)
The Young’s double slit experiment is an example of ___________, and can be expanded by, e.g., considering the case where the amplitudes of light through slit 1 and slit 2 are not equal, to yield a lower visibility of the fringes V = __________________
- interference by wavefront division
- (Imax − Imin)/(Imax + Imin)
An alternative form of interference is by ________, e.g., ________________
- amplitude division
- double reflection from a thin film
Generally speaking, constructive interference results when the (optical) path difference for light following two different path Γ = __, with integer m; and destructive interference when Γ = ______.
- Γ = mλ
- Γ = (m + 1/2)
Upon reflection from the boundary towards an optically denser medium (__________), the light acquires a phase shift of __, equivalent to an additional ____; hence in general, phase shift on reflection may be relevant for determining conditions of constructive and destructive interference.
- from lower to larger n
- π
- 1/2 λ
For a thin film, one can show that Γ = _______, with d ___________, n its __________, and β_____________ (with respect to the surface normal) in the film. Hence for perpendicular incidence (cos β = 1) Γ is simply n × 2× the film thickness.
- 2nd cos β
- the thickness of the film
- its index of refraction
- the angle of the light path
Relevant examples of thin film interference are ____________________________________.
anti-reflection coatings, wedges, and Newton’s rings.
Spatial coherence is __________________________________________, i.e., over what distance the phase change is given by ∆φ = (2π/λ)∆x
- the distance one goes along a wave with constant separation of peaks and troughs
Temporal coherence is _____________________________________________________________________________________________________, i.e., for how long ∆φ = ω∆t.
a measure of how long a wave at a particular point maintains a distinct phase relationship between equivalent parts of the wave
In the Michelson interferometer, an appropriate arrangement of mirrors allows light to follow two different paths that are next recombined, and interference depends on the ______________, as usual, and the interference pattern can be calculated by __________________________________.
- optical path difference
- summing the waves in complex notation.
