5 - Diffr/Thin Film/Scatter/Polar

Question 1

Describe scatter + types (2)

Answer 1

Bending of waves around obstacles

Fraunhofer: far-field

Fresnel: near-field

Question 2

Diffraction and resolution ability

Answer 2

Resolution is limited by diffraction

As light passes thru a circular aperture, it creates an Airy disk
-larger for smaller apertures
-2 objects cannot be distinguished when the 2 corresponding Airy disks overlap
—mathematically = Rayleigh’s criteria

Question 3

How we estimate pt’s expected VA thru pinhole

Answer 3

Rayleigh’s criteria: sinθr = (1.22λ)/d

Rayleigh’s criteria for pinhole: assumes λ of 555nm, θ corresponds to MAR, d is pinhole diameter in milimeters, we rewrite Rayleigh’s as:
MAR = 2.33/d (mm)
*d of 2.3 = 20/20 vision

Recall:
MAR: (Snellen fraction)^-1
-units arc minutes

Question 4

Anti-glare coatings

Answer 4

AR = thin film that creates destructive interference between 2 reflecting light waves

We choose the film so that nL > nF > 1 (lens > film > 1)

Question 5

Minimum film thickness providing destructive interference for anti-glare coatings equation

Answer 5

d = λ/(4nf)

Thickness = wavelength of light/(4*index of refr of film)

If not specified, assume 555nm for wavelength

Question 6

Optical thickness equations (2)

Answer 6

OT = (d)(nf) = (thickness of film)*(index of refr of film)

OT = λ/4

*second one is much more helpful!

Question 7

Ideal thin film equation (film material that minimizes reflection)

Answer 7

nf = √(n1nL)

Index of film = √((index of initial medium)*(index of lens material used))

Initial medium usually air

Question 8

Describe Rayleigh scattering and give equation

Answer 8

Particles that cause are much SMALLER than the wavelength of light = WAVELENGTH-DEPENDENT
-gives sky blue color, sunsets red

I ∝ 1/(λ^4)

Intensity of scattered light = 1/(wavelength to the fourth)

Question 9

Describe Tyndall scattering

Answer 9

Particles that cause are much LARGER than the wavelength of light and is PURELY DUE TO GEOMETRIC OPTICS = WAVELENGTH-INDEPENDENT
-gives clouds white color

Question 10

Light consists of oscillating (2) field vectors, both perpendicular to the direction of travel.
Polarization allows us to talk about the shape that __ vector traces out in that plane.

Answer 10

E (electric) + B (magnetic)

E

Question 11

Describe linearly polarized light

Answer 11

Oscillations of the E vector (in time) all fall on a line

The magnitude of E is changing, but direction is constant

Question 12

Describe circularly polarized light

Answer 12

Oscillations of the E vector (in time) trace out a circle
The E vector is rotating, but its magnitude is constant

Mathematically due to addition of 2 linearly polarized waves of EQUAL AMPLITUDE and a phase difference of θ = π/2

Question 13

Describe elliptically polarized light

Answer 13

Oscillations of E vector (in time) trace out an ellipse
The E vector is rotating AND changing in magnitude

Mathematically due to addition of 2 linearly polarized waves of DIFFERENT AMPLITUDE and a phase difference of θ = π/2

Question 14

Describe Brewster’s law

Answer 14

Reflection changes the state of polarization of light

Directly applied in polarized sunglasses
-in particular, made to reduce glare arising from horizontal surfaces

Question 15

Polarizers

• absorption axis
• transmission axis

Answer 15

AA: parallel to the wire grid, E field components parallel to the AA are not transmitted

TA: perpendicular to the wire grid, E field components parallel to the TA are transmitted

Question 16

Polarizers

-when unpolarized light is incident on a polarizer, the intensity of the light transmitted is __

Answer 16

Half of the incident light:

I = (I0)/2

Question 17

Polarizers

-describe Malus law

Answer 17

When plane polarized light is incident on a polarizer, ML gives the intensity of the transmitted light as:
I = I0cos^2(θ)
Intensity of transmitted light = intensity of incident lightcos squared(angle b/w incident polarization and trasmission axis of polaroid)

Note: in the special case where the incident polarization and the transmission axis of the polaroid are separated by 45 degrees, the ML simplifies to I = I0/2