Optics Flashcards
What is Fermat’s Principle?
Also known as principle of least time - Of all the possible paths that a ray of light may take to get from one point to another, light takes the path which requires the shortest time. Use mirror example to explain.
Define incident angle and refracted angle
The angle between the path coming in and the vertical we shall denote θi which is called the incident angle, while the angle between the vertical and the refracted line shall be denote θr. This is called the refracted angle.
What is the formula for Snells Law (incident = refracted)
n1 sin θi = n2 sin θr
What is the formula for refractive index?
ni = c/vi
What is the principle of least action
a quantity called an action was being minimized by the choice of paths.
What is total internal reflection?
Well what we find is that the light ray stops transmitting through the boundary, and reflects back
What is the critical angle and its formula?
sin θc = n2/n1 -> This defines what we call the critical angle. The angle that if you go past, you will get total internal reflection.
Dispersion
Refraction ultimately involves the interaction of electromagnetic waves with atomic electrons
We generally consider air’s refractive index to be 1, close to a vacuum, and then the refractive index of a glass prism, is dependent on the wavelength where 1 < n(λred) < n(λyellow) < n(λblue)
This means if we consider Snell’s Law, then the refracted angle is going to be smaller, so therefore the light bends more for blue light with its larger refractive index, than red light with its smaller refractive index.
Define diffraction
The bending of a wave as it pass by objects
What is Huygens Principle?
All points on a wavefront act as point sources of spherically propagating “wavelets” that travel at the speed of light appropriate to the medium. At a short time later the new wavefront is the unique surface tangent to all the forward propagating wavelets
Where you have diffraction around a corner and through a wide gap and small gap
What is coherence and interference?
Steady interference patterns occur only when waves maintain a constant phase relation, and we call these waves coherent waves.
Note: It is notoriously difficult to get two waves to be coherent from two different sources, even with lasers. So when we want a steady predictable interference pattern, its usually better to get a single source then split the light up, and recombine somehow elsewhere. These two waves should now be coherent.
What happens if the two paths the different coherent waves take are of different lengths?
One of the waves when they meet back up again might not be all the way through the same wave pattern. This is going to mean when they meet up at the same spot they interfere. If they are completely out of phase with each other they will completely destructivevly interfere. Or more correctly they destructively interfere at a particular point in space where they meet. If this is light, you will get a dark spot there, as the light has destructively interefered. So a question to ask is what path difference would do this? Well it turns out destructive interference occurs in coherent light, when the path length differs by an odd multiple of half the wavelength. As you could imagine, the even multiples, that is the path differences of integer multiples of the wavelength will have the opposite effect. They will produce constructive interference.
Define interference pattern
a series of bright spots, separated by dark patches
Formula for Bright and Dark fringes (double slit)
d sin θ = mλ, m = 0, 1, 2, … bright fringes, double slit
d sin θ = (m + (1/2))λ, m = 0, 1, 2, … dark fringes, double slit
What is diffraction grating and its formulas?
d sin θ = mλ, m = 0, 1, 2, … bright maxima, N slits
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d sin θ = (m/N)λ, dark minima, N slits
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