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Chapter 17 & 18: Light - Coggle Diagram

- - - - The Wave Model
        
        Many properties of light act as a wave(i.e. sound or water). Study of this is called wave optics
        
        When a wave passes between to objects that are spread apart widely it continues moving forward
      - The Ray Model
        
        Telescope, Mirrors, Lenses, etc are considered to move in a straight path referred to as Light Rays, or Ray Optics
      - The Photon Model
    - - Diffraction
        
        Light passing through an object's opening is a wave
    - - All electromagnetic waves and light waves travel at the same speed(Speed of Light): v_light = c = 3.00 * 10^8 m/s. Nothing can be more than this
    - - The wave's frequency doesn't change as it moves from one material to another
        
        The material's basis
        
        Wavelength in transparent material is shorter than in a vacuum in order to maintain frequency
      - Example: In comments
      - Number of wavelengths equation: N = d / λ. (d) being the span of distance of N
        
        https://gyazo.com/d4e19648a5a1ae662a05de17a2e44c0e (Answer in comments)
    - - The speed of light in a material is based on the material's index of refraction n
        
        n = speed of light in a vacuum (c) / speed of light in the material (v)
        
        material's Index of refraction
        
        A vacuum has n =1, Air = 1.0003, Water = 1.33,Glass = 1.50, Diamond = 2.42
  - - - To observe interference, we need two light sources whose waves can overlap and interfere. The experiment is a laser beam aimed at an opaque screen containing two long, narrow slits that are very close together.
    - - constructive interference between two waves from identical sources occurs at points for which the path-length difference Δr = r2 - r1 is an integer number of wavelengths, which we can write as
        
        Δr = mλ ; m = 0, 1, 2...
      - point P can be specified by either its distance y from the center of the viewing screen or by the angle θ; angle θ and distance y relate as
        
        y = Ltanθ
      - a right triangle can be found by Δr or path-length difference between the two waves is the short side of this triangle, in relation to d the slit spacing
        
        Δr = dsinθ
      - Final equation is written as:
        
        Δr = dsinθ_m = mλ ; m = 0, 1, 2...
        
        sinθ_m = m(λ / d) ; m = 0, 1, 2...
        
        Angles of bright fringes due to a diffraction grating with slits distance d apart
        
        The light waves from the slits will be in phase of each other and arrive at some point on the screen
      - Positions of bright fringes for double-slit interference at screen distance L
        
        y_m = (mλL / d) ; m = 0, 1, 2...
        
        Spacings between two adjacent bright fringes
        
        Δy = (y_m + 1 - y_m) = ((m + 1)λL / d) - (mλL / d)
        
        Δy = λL / d
      - Positions of dark fringes for double-slit interference
        
        Δr = (m + 1/2)λ ; m = 0, 1, 2...
        
        y'_m = (m + 1/2)(λL / d) ; m = 0, 1, 2...
      - Question: Light of wavelength λ1 illuminates a double slit, and interference fringes are observed on a screen behind the slits. When the wavelength is changed to λ2, the fringes get closer together. Is λ2 larger or smaller than λ1? Answer in comments
  - - - The science of measuring the wavelengths of atomic and molecular emissions
        
        Bright fringes are so distinct, diffraction gratings are an ideal tool for this
    - - It is a mirror with hundreds or thousands of narrow, parallel grooves cut into the surface.
      - The incident light that hits the grooves is diffracted at different angles and are overlapping eachother
    - - a multi-slit device is called a diffraction grating. The light intensity pattern on a screen behind a diffraction grating is due to the interference of N overlapped waves.
        
        With diffraction grating the angles for the bright fringes aren't small so small angle approximation can't be used
        
        Instead the y_m and mth maximum turn into y_m = Ltanθ_m
        
        This equation is the position of bright fringes due to a diffraction grating distance L from screen
        
        This equation applies to reflection gratings and the transmission ones as well
    - - For example: A commercial diffraction grating has 500 lines per mm and laser is shot at it at 480 nm. The 500 lines per mm is rewritten into meters which is 2e-6 and 480nm into 4.80e-7. The equation is then finding m
        
        m is then equal to 4 but this isn't the correct answer to find the bright spots you use the following: N = 2m + 1
        
        Answer: 9
- - - - Light Rays don't interact when crossing over (Don't affect eachother)
      - Light Rays go on forever until they hit matter(an object)
        
        They can be reflected(Diffuse Reflection) or refracted when hitting a material
        
        They can scatter(Broken into weaker rays) or be absorbed when inside a material
        
        Sources of Light Rays
        
        A point sources
        
        Emits light in every direction. Bulbs are the closest to these
        
        An extended source
        
        every point of an extended source acts like a point source(ex: lightbulbs, flames and the sun)
        
        A parallel-ray source
        
        A bundle of parallel rays, flashlights and movie projectors
        
        A ray source
        
        A thin beam laser is a good approximation of a single ray
      - Objects
        
        objects are a source of light rays from all points of an object that send out in all directions
        
        Objects could be self-luminous or be reflective/illuminated
      - When an eye sees an object it diverges the light rays
        
        Seeing Objects
        
        For example you can't see a laser beam in the air until hits an object(In some cases if it hits smoke or dust than it can be visible in the air)
    - - The small amount of rays shown are a just a few of the infinitely many rays
    - - Some rays hit the objects and hit the object behind it luminating it casting a shadow
      - Point source gives a hard shadow while an extended source doesn't create a sharp shadow
  - - - θ_i is called the angle of incidence and is between the incoming ray(incident ray) and the normal line
        
        The angle of incidence(θ_i) equals the angle of reflection(θ_r) (Law of Reflection)
      - θ_r is the angle of reflection and is between the normal line and the reflected ray
      - Example Problem: https://gyazo.com/34d33632a39fcea6d6db044ade679d60
        
        All angles are the same due to the law of reflection: θ = tan^-1(0.5 m / 1.0 m) = 26.6°
        
        (Length) l = 2.0 m / tan 26.6° = 4.0 m
    - - Obeys law of reflection but the rays of light spread out when reflecting
        
        Ex: https://gyazo.com/8f06a61505a9e521e342cd0426c4b9f7
    - - Example of a Plane Mirror: https://gyazo.com/70813d84a159c1b2de5fc0d2bea662b8
        
        How our eyes see the reflected image from mirror: https://gyazo.com/5512800f476fde006602d7cb20e0223e
        
        Important Notes:
        
        Not all rays will hit your eye due to how they're reflected but others you can't see might be seen by another person
        
        Example of multiple rays coming from different points: https://gyazo.com/0735b8105286dfd0a1eae827c53c5deb
        
        Question: https://gyazo.com/a7602126f3dcc96963b7d360aa2d2153 (Answer in Comments)
        
        You can't see the full image of an object in a very small mirror since the rays are reflected from different areas missing your eyes
  - - - Light reflects from boundary although being transparent(like store front windows) and obeys the law of reflection
      - Light hits the medium in the object and changes direction referred to as a transmission this phenomenon is called Refraction
        
        Ex: https://gyazo.com/a8a2216b466cd8024f2b5c5a0746d38e
    - - If the ray moves from medium 1 to medium 2 it bends closer to the normal line while from medium 2 to medium 1 to bend away
        
        Steps to solve problems: https://gyazo.com/e7b74e57ec758f1166b1c0b50e4e5b1c
      - Higher index of refraction, bends into a smaller angle with the normal. Lower index bends into larger angle with normal.
      - If the sin of an angle is greater than 1 then refraction cannot be possible under rules of Refraction since 100% of light would reflect back into the boundary
        
        This case is referred to as Total Internal Reflection(TIR)
        
        Drawing Ex: https://gyazo.com/ae7a338f90a1b24d61c39a875f644398
        
        Back to Snell's Law (n1sinθ1 = n2sinθ2), θ1 becomes θ1 = sin ^-1(n2 / n1) when θ2 = 90°
        
        Real life uses: https://gyazo.com/1d98acbe7f73bd9031f20d7f7e3b5e83
    - - The speed of light and the index of refraction determines a light rays speed in a medium: v = c/n
      - Chart of different mediums: https://gyazo.com/be22b5f8e8420a4a8485c3154e6a8f93
      - Snell's Window: https://gyazo.com/ddc77dda8dbe37d81107aa4c9c0b76cd
  - - - P' is closer because of the refraction of the light
        
        P' is also referred to as a virtual image(meaning not real)
    - - s' = (tanθ1 / tanθ2) * s
        
        Snell’s law relates the sines of angles and ; that is,
        
        (sinθ1 / sinθ2) = (n2 / n1)
        
        We can find the image distance from the previous equation
        
        s' = (n2 / n1) * s
  - - - Definition of lens: A transparent object with curved surfaces to produce an image using refracted light rays
        
        A converging lens makes rays refract towards the optical axis
        
        Both their focal lengths are the distance from the point which the rays parallel to the optical axis converge or diverge from which they appear to .
        
        Diverging lens, causes the rays to refract away from the axis.
      - The distance of the focal point from the lens is called the focal length f of the lens.
        
        The focal point and focal length of Converging and Diverging Lens: https://gyazo.com/e46edd9e2aa4f3098703e9e86c5db138. This image shows that all incoming rays initially parallel to the optical axis converge at the same point, the focal point of the lens
        
        Converging Lens
        
        Diverging Lens
  - - - Converging Mirrors/Concave Mirror
        
        Edges of mirror curve towards the light source
        
        law of reflection then tells us that the incoming ray will reflect at the same angle, but on the opposite side of the optical axis.
        
        Example
        
        parallel rays reflect off the mirror and pass through a single point or were brought together at a focal point, as was the case for a converging lens
        
        how they reflect
      - Diverging Mirrors/Convex Mirror
        
        Edges of mirror curve away the light source
        
        rays of light appear to diverge from a focal point behind the mirror, and will produce virtual images similar to what diverging lenses do.
        
        https://gyazo.com/e914e9aa8db21facbe1c40043d3ec890
  - - - "s" is the distance the actual object is away from the lens/mirror
      - s' is the distance the image produced is away from the lens/mirror
      - "f" is typically the product of "s" and s' and is the actual focal length of the lens/mirror
      - Thin-Lens Equation in reference to height of images: h'/h = (s' - f) / f || h'/h = s'/s