Optics

Geometric Optics:

Geometric Optics

When waves of light (or electromagnetic waves in general) hit the boundary between two media, there are several ways that the light can react. Namely, it can reflect, refract, or be absorbed into the second medium. These will be explained below.

n1sin(θ1) = n2sin(θ2)

I. Reflection - Reflection occurs when light (or any wave) hits a surface and bounces back into the medium it originated from.

  • The angle of incidence of a wave or stream of particles reflecting from a boundary, conventionally measured from the normal to the interface, is equal to the angle of reflection, measured from the same interface.

II. Refraction- Refraction is the bending of light as it passes between two mediums with different optical densities (e.g., air and water).

  • How light transmission varies when traveling through a medium

Optical density

  • The optical density of a medium measures how well it can transmit light. Water has a higher optical density than air, so light travels slower in water than it does in air. Note that optical density is different than the actual density of a medium.

Specular & diffuse reflection

  • Specular reflection occurs on smooth surfaces like mirrors, while diffused reflection happens on rough light, scattering light in many directions

Law of Reflection 

  • Law: The angle of incidence (incoming light) of a wave or stream of particles reflecting from a boundary, conventionally measured from the normal to the interface, is equal to the angle of reflection (bounced light), measured from the same interface.

  • Reflection requires a "wave or stream of particles" and an interface (mirror)

Index of refraction

  • A method of characterizing the refraction of light, defined as the ratio of the speed of light in a vacuum to the speed of light in the medium. The refractive index can be calculated using Snell’s law.

Snell’s law

  • Part of refraction

  • --> Equation 

    • n1 = refraction

  • The index of refraction is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium.

  • Critical Angle and Total Internal Reflection:

    • Critical angle: The smallest angle of incidence for which light is completely reflected within the denser medium.

    • Total Internal Reflection: Occurs when the angle of incidence exceeds the critical angle (e.g., in fiber optics).

III. Prisms, Mirrors, and Lenses

These tools manipulate light for specific purposes.

  • Prisms:
    Separate white light into its spectrum (dispersion) and change the direction of light (deviation).

    • Dispersion: when white light is allowed to pass through a prism; it gets refracted into seven colors.

    • Deviation: How the beam of light in a prism changes its route via refraction.

  • Mirrors:

    • Convex (Diverging): Bulges outward; reflected rays spread apart. Used in security mirrors.

    • Concave (Converging): Curves inward; reflected rays converge at a focal point. Used in telescopes and makeup mirrors.

  • Lenses:

    • Convex (Converging): Thicker in the center; focuses light to a point (e.g., magnifying glasses).

    • Concave (Diverging): Thinner in the center; spreads light out (e.g., for correcting nearsightedness).

    • The six lens types are: plano-convex, plano-concave, double convex, double concave, concavo-convex, and convexo-concave.z


III. Color theory: Additive & subtractive color theory; primary & secondary colors; absorption &

  • Additive: Additive mixing occurs in light, such as on a computer screen where red, green, and blue are mixed in different proportions to create other colors. 

-Yellow is made of red + green

-Magenta is made of red and blue

-Cyan is made of green and blue

- Subtractive: Subtractive mixing occurs with physical dyes, like in printing or in paints. 

-When cyan, magenta, and yellow dyes are mixed, only the primary colors in common are visible

-Yellow and magenta form red, cyan, and yellow for green, and cyan and magenta form blue

  • Primary colors: red, green, blue

  • Secondary colors: yellow, magenta, cyan


Another consideration is colored filters. A colored filter will transmit only the colors of light required to form that color. Therefore, a cyan filter would absorb red light, while transmitting blue and green light, and a red filter would absorb both blue and green light while transmitting red light.


Complementary colors are 2 colors that create black ( for subtractive ), or white ( for additive ). So, for example, additive light, red and cyan are complementaries because those 2 colors together will create white, as cyan is both green and blue -- the other 2 primary colors that arent red. So, complementary colors will be a primary color, and a secondary color made up by the other 2 primarys.


Another thing that may show up on tests are questions like " What colors will a [ ] shirt reflect and absorb?" and its the same logic as colored filters, except instead of colors being passed through, theres colors being reflected off the shirt. So a blue shirt would reflect blue and absorb red and green, and so on.



IV. Optical Properties and Images

  • Virtual Images: Cannot be projected; appear upright and are formed by diverging light rays (e.g., behind mirrors).

  • Real Images: Can be projected onto a screen; appear inverted and are formed by converging rays.

  • Magnification: Ratio of the image size to the object size.

  • Erect images: In optics, an erect image is one that appears right-side up. An image is formed when rays from a point on the original object meet again after passing through an optical system. In an erect image, directions are the same as those in the object, in contrast to an inverted image. 

V. Structure and Function of the Human Eye

  • Cornea: Clear, outermost part; bends light significantly.

  • Lens: Fine-tunes focus by changing shape (accommodation).

  • Retina: Contains photoreceptors (rods and cones) that convert light into neural signals.

    • Rods: Sensitive to low light; perceive brightness and grayscale.

    • Cones: Detect color; function well in bright light.

  • Optic Nerve: Transmits visual information to the brain for processing.

  • Macula: Responsible for detailed central vision (e.g., reading).

  • Cones: The color receptors of the eye. Cones are used more during daytime when colors are more vibrant and pronounced. There are 7 million cones in the human eye.

    • There are 3 types of eye cones (Blue, Green, and Red)

      • Other animals like Mantis shrimp can see more colors because they have more cones, meaning we cannot see the forbidden shrimp colors




     Structure and function of the human eye


  • Cornea: The transparent part of the eye covering the iris and pupil. The cornea refracts light, providing about two-thirds of the eye's optical power.


  • Iris: The iris controls the size and diameter of the pupils, which serves to adjust the amount of light that enters the retina.


  • Lens: The lens helps to refract light and focus it onto the retina. It changes shape to adjust its focal distance so that the eye can focus on objects at different distances.


  • Macula: The macula in the human eye is the place where light is focused by the structures in the front of the eye (cornea & lens). It takes the picture that is sent to the brain, where vision is completed. The macula provides us with the ability to read and see in great detail whereas the rest of the retina provides peripheral vision.


  • Optic Nerve: The optic nerve sends information from the retina to the brain so that it can be processed.


  • Optic Disc: The raised disk on the retina at the point of entry of the optic nerve, lacking visual receptors and so creating a blind spot.


  • Retina: The retina lines the inner surface of the eye and creates images based on the light passing through the eye. These images are then sent to the brain via the optic nerve.


  • Rods: The photoreceptors of the eye. Rods sense brightness and are favored during nighttime, when color is mostly absent and objects are viewed on a grayscale. There are 120 million rods in the human eye.


  • Sclera: The white outer layer of the eyeball. At the front of the eye it is continuous with the cornea.







Some possible diseases the eye can get are:

  • Cataracts- Doesn’t cause pain, redness, or tearing. When the inner lens of the eye becomes darkened or opaque, the condition is called a cataract. The lens may be surgically replaced with a plastic lens. The implanted lens is of fixed focal length, so it is not capable of accommodation like the natural lens. This is usually not a major concern, because persons who develop cataracts after age 60 do not have much accommodation remaining because the inner lens has become less pliable with age.

  • Myopia- nearsightedness; rays converge in front of the retina. Corrected with a diverging lens.

  • Hyperopia-  farsightedness; rays converge behind the retina. Corrected with a converging lens

  • Astigmatism- irregularly shaped cornea; in some cases caused by lens (lenticular astigmatism). Corrected with eyeglasses; astigmatism causes near and farsightedness.

  • Aphakia- the absence of the lens of the eye. It causes a loss of accommodation, farsightedness (hyperopia), and a deep anterior chamber. Complications include detachment of the vitreous or retina, and glaucoma.

  • Glaucoma- A group of diseases that damages the optic nerve. This can be due to an infection or other critical conditions and may lead to blindness if not cured early. It is due to a build-up of pressure in the eye.

  • Presbyopia- Presbyopia is a condition associated with aging of the eye that results in progressively worsening ability to focus clearly on close objects. Presbyopia is a natural part of the aging process. It is due to hardening of the lens of the eye causing the eye to focus light behind rather than on the retina when looking at close objects

  • Amblyopia-  A type of eye disease that is commonly referred to as a "lazy eye". This is generally due to a nerve pathway being damaged in the brain during childhood and may lead to blindness if not treated early.


VI. Lens maker’s equation & thin lens approximation


f = focal length

u = object distance

v = image distance


VII. Polarization: films & scattering, Brewster’s angle

  • Polarized Lenses

vii. State & National Only:

viii. Basic 2D geometry required for ray tracing. For example, parallel & perpendicular lines, rays, triangles (similar & congruent), and circles

ix. Simple algebra manipulations, including solving one equation for one variable


6.63 * 10^-34  = Planck’s Constant

2.998 * 10^ 8 m/s = speed of light ©


Spectroscopy: 


Spectroscopy is the study of light and how it works in relation to absorption spectra, the EM Spectrum, etc


Spectra are an application of the visible light spectrum to specific materials. Since certain materials have a unique absorption spectrum and emission spectrum associated with them, spectra can be used to identify unknown materials. They can also be used to learn more about materials at a microscopic level, including things such as molecular structure, crystal structure, and purity.


There are two types:

  • Absorption spectra

  • Emission spectra


Laser Shoot: 


Objective of Laser Shoot: 

Competitors will use up to 5 mirrors to reflect a laser around a barrier/barriers to get as close as possible to a target point. 25 points will be awarded based on the accuracy of the laser, and the other 25 points will be awarded based on the mirrors used to reflect the laser - 4 points each for the 5 movable mirrors, and 5 points for successfully using the fixed barrier mirror.

The Laser Shoot takes place in the Laser Shoot Setup, or LSS. This setup must be the same for all teams. The LSS is enclosed by a rectangular field of approximately 35 cm by 56 cm, with an open top such that students can place and adjust mirrors. A laser is placed at the center of one of the short sides, such that the laser beam is normal to the wall. On the opposite wall, a Target Point is marked at the same height as the laser, although not necessarily at the center of the wall. In both divisions, a barrier must be placed at any point along the centerline (the unrestricted path of the laser) of the LSS, such that the barrier is tall enough to block the laser and mirrors can feasibly be placed to deflect the laser beam. In Division C, two additional barriers are placed at any position in the LSS. In Division B, the barrier must have a mirror attached to one side, while in Division C, any of the barriers may hold the mirror.




Lenses and Mirrors

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Spectra

-Absorptive Filter: Glass or plastic filters absorbing specific light wavelengths.

-Dichroic Filter: Reflective cavities cancel specific wavelengths via interference.

-Interference Filter: Expensive, delicate filters using interference for wavelength selection.

-Long-Pass Filter: Transmits longer wavelengths, attenuates shorter ones.

-Short-Pass Filter: Transmits shorter wavelengths, attenuates longer ones.

-Bandpass Filter: Transmits wavelengths within a specific interval.

-Monochromatic Filter: Allows only a narrow range of wavelengths.

-Infrared Filter: Allows infrared light or blocks it in projectors.

-Ultraviolet Filter: Blocks UV rays, transmits visible light in cameras.

-Polarizer Filter: Blocks light based on polarization, used in sunglasses.

-Absorption Spectra: Wavelengths absorbed by a material, useful in analysis.

-Emission Spectra: Wavelengths emitted when electrons are excited.

-Gel Filters: Plastic filters with compounds for specific light absorption.

-Reflective Cavities: Structures in dichroic filters resonating with specific wavelengths.

-Destructive Interference: Cancellation of specific wavelengths in dichroic filters.

-Chemical Analysis: Using absorption spectra to determine star composition.

-Star Composition: Determined via emission spectra from excited electrons.

-Ultraviolet Bandpass Filter: Less common filter allowing specific UV wavelengths.

-Polaroid Material: Used in polarizer filters to block polarized light.








Extra Vocabulary

Aperture: Describes how much light will be intercepted by the mirror.

Center of curvature: Useful when locating images, the center of the imaginary sphere upon which a curved mirror rests. The flatter the mirror, the farther away the center of curvature.

Concave mirror: Converging mirror which forms either real or virtual images which may be magnified.

Convex mirror: Diverging mirror which forms virtual images which may be magnified.

Focal length: The distance from the lens or mirror to the principal focus.

Principal axis: The main line drawn through the center of the mirror or lens upon which information such as center of curvature or principal focus is given.

Principal focus: The point where light rays parallel and close to the principal axis converge or appear to diverge.

Ray diagram: A tracing of the light rays to show where the image forms after being reflected off a mirror or refracted through a lens.

Real image: An image that can be projected onto a screen at its location, inverted relative to the object, and can be magnified.

Secondary axis: Any line drawn through the center of curvature to the mirror or lens.

Vertex: The center of a lens or mirror.

Virtual image: An image that cannot be projected onto a screen, is not inverted relative to an object, and can be magnified.