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GEOMETRICAL OPTICS - Coggle Diagram

- - - - Plane waves with flat wavefronts arriving at a thin lens are curved to stay isochronous.
  - - - The object and image distances are measured from the focal points like the picture.
        The equation is simpler and is used in certain applications:
        m = hi/ho = f/x = x'/f, yields xx' = f^2, where i & o are subscripts respectively.
- - - - Image properties of a point object: 1. Image distance = object distance. 2. Image is virtual (no actual rays intersect to build the image). 3. Image cannot be projected on a screen.
      - Image properties of an extended object: 1. Image size = object size or magnification = 1 2. Transverse orientation of image and object are the same. 3. A right‐handed object has a left‐handed image 4. Image location does not depend on the observer.
  - - - First order approximation (paraxial)
        
        From the figure we can write:θ=α + Φ; 2θ = α + α' The relationship has to be independent of the ray we choose to trace so we have to eliminate
        θ between the two equations: We get: α - α' = -2 Φ
        
        Paraxial approximation
  - - - Sign convention
        
        For real objects and images the distances are positive.
        For the virtual objects and images the distances are negative.
        Or: real positive, virtual
        negative
      - Focal lengths
        
        the image distance for the object at infinity and
        object distance for the image at infinity (figures).
        The general equation for the spherical mirrors:
        1/s +1/s' = 1/f
        f = -R/2 ===== >0 concave mirror, <0 convex mirror.
    - - Sign convention:
        (+) when image and object have the same orientation. (‐) when image and object have
        opposite orientation.
- - - - a) Extension of the rays emerging from point object S do not converge to an image point.
        b) Using the paraxial optics approximation i.e. working with the rays that remain close to the
        central axis i.e. sin θ ≈ tan θ≈ θ ≈60 ≈ 0.1 radians, we can observe an image of S at S’.
      - From Snell's law for paraxial rays we can write:
        n1 tan θ1 = n2 tan θ2 analogous to n1(x/s) = n2 (x/s')
        Location of the image point: s' = (n2/n1) s
        -If n2> n1 then s ' > s and the image forms below the object point. Apparent depth is larger
        than the reality (seeing objects from a pool) .
        -If n2 < n1 then s ' < s and the image forms above the object point.Apparent depth is smaller
        than the reality (looking into water).
  - - - Formula for the location of image:
        Using the Snell's law we have : n1 sin θ1 = n2 sin θ2
        In the triangle CPO:
        α = θ1 + Φ , θ1 = α - Φ
        In the triangle CPI:
        α' = θ2 + Φ , θ2 = α' - Φ
        Using the paraxial approximation and replacing the sines in the Snell's law with the value of
        the angles in radian we get:
        n1 (α - Φ )= n2 (α' - Φ )
    - - m = hi/ho = -n1s'/ n2s, o & i, 1 & 2 are subscripts.
        For a plane refracting surface
        s' = - (n2/n1)s & m = - n1/n2s((-n2/n1)s) = +1
- - - - We use the same sign convention as the spherical lenses.
        AB image length is always positive CL length of lens along the axis of cylinder.
        From the similar triangles:AB/CL =( s + s' )/sAB =((s+ s')/s))CL