4D: Geometrical Optics
Lensmaker's Equation
1/f = (n-1)((1/r1) - (1/r2)) Note: Used for lenses with non-negligible thickness
Multiple Lens System Equations (In Contact)
1/f = 1/f1 + 1/f2 + 1/f3 + ... + 1/fn P = P1 + P2 + P3 + ... + Pn
Key Variables in Geometrical Optics
1/f = 1/o + 1/i = 2/r f: Focal Length o: The Distance Between the Object and the Mirror i: The Distance Between the Image and the Mirror r: Radius of Curvature (Distance Between C and the Mirror)
Hyperopia
A condition in which visual images come to a focus behind the retina of the eye and vision is better for distant than for near objects -- called also farsightedness. Note: A lens using a convergence of light is needed to correct farsightedness
Ray Diagram
A diagram showing rays that can be drawn to determine the size and location of an image formed by a mirror or lens
Magnification (m)
A dimensionless value that is the ratio of the image distance to the object distance: m = -(i/o) Note: |m| < 1: Reduced (The image is smaller than the object) |m| > 1: Enlarged (The image is larger than the object) |m| = 1: The image is the same size as the object
Plane Mirrors
A flat mirror; reflecting surface that has no curvature. It always creatures virtual images.
Converging Lens
A lens that is thicker in the middle than at the edges and that refracts parallel rays to a focus. Also known as a convex lens.
Diverging Lens
A lens that is thinnest in the middle causing light rays to spread apart. Also known as a concave lens.
Normal
A line perpendicular to the boundary of the medium.
Index of Refraction
A measure of the amount a ray of light bends when it passes from one medium to another. n = c/v n: Index of Refraction c: Speed of Light in a Vacuum v: Speed of Light in the Medium
Specular Reflection
A reflection produced by a smooth surface in which parallel light rays are reflected in parallel
Critical Angle (θc)
A special incident angle, for which the refracted angle θ2 is equal to 90º. θc = sin^-1 * (n2/n1)
Chromatic Aberration
A spherical lens defect in which light passing through a lens is focused at different points, causing an object viewed through a lens to seem to be ringed with color (rainbow halo)
Virtual Image
An image that forms at a location from which light rays appear to come but do not actually come
Real Image
An image that is formed by the intersection of light rays; a real image can be projected on a screen
Upright Image
An image that is oriented in the same direction as the object. ("right-side-up"). A positive magnification.
Inverted Image
An upside down image. A negative magnification.
Converging Mirrors
Cause parallel incident light rays to reflect convergingly. Another name for concave mirrors.
Diverging Mirrors
Cause parallel incident light rays to reflect divergingly. Another name for convex mirrors.
Convex
Curved Outward
Aberrations
Departure from what is normal
Focal Length (f)
Distance from the focal point to the center of a lens or vertex of a mirror Note: For all spherical mirrors, f = r/2
Center of Curvature (C)
It is the center of the imaginary sphere upon which a curved mirror rests, the flatter the mirror, the farther away the center of curvature
Focal Point (F)
Location at which rays parallel to the optical axis of an ideal mirror or lens converge to a point
Spherical Mirrors
Mirrors that have centers (C) and radii (r) of curvature as well as focal points. Come in concave and convex varieties.
Myopia
Nearsightedness; lack of foresight. Note: A lens using a divergence of light is needed to correct nearsightedness
Power (P)
P = 1/f P: Power f: Focal Length
Sign Conventions for Mirrors
Refer to Table
Sign Convention for a Single Lens
Refer to table
Diffuse Reflection
Reflection that occurs when parallel rays of light hit a rough surface and all reflect at different angles
Concave
Rounded inwards
Refraction
The bending of light as it passes from one medium to another and changes speed.
Reflection
The bouncing back of a ray of light, sound, or heat when the ray hits a surface that it does not go through. Law of Reflection: θ1 = θ2 θ1: Incident Angle θ2: Reflected Angle
Total Internal Reflection
The complete reflection of light by the inside surface of a medium. Results with any angle of incidence greater than the critical angle.
Radius of Curvature (r)
The distance from the center of curvature to the mirror
Image Distance
The distance from the mirror to the image. If it is positive then it is a real image, and if it is negative than it is a virtual image. Note: For plane mirrors, r = f = ∞ --> 1/o + 1/i = 0 or i = -o
Spherical Aberration
The image defect of a spherical mirror that does not allow parallel light rays far from the principal axis to converge at the focal point, and produces an image that is fuzzy, not sharp.
Axis
The normal passing through the center of a mirror.
Snell's Law
The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, for a given frequency. n1 * sinθ1 = n2 * sinθ2 or v1/sinθ1 = v2/sinθ2 n1 and sinθ1: Refer to Medium From Which the Light is Coming n2 and sinθ2: Refer to Medium Into Which the Light is Entering Note: θ is measured with respect to the normal
Lenses
Transparent pieces of glass or plastic used for refracting light.
Diopters
Units used to express the power of a lens; diopters = 1/(focal length). Note: Also can be defined as 1/(m)eters or m^-1
Rectilinear Propagation
When light travels through a homogenous medium, it travels in a straight line
Dispersion
When various wavelengths of light separate from each other. This is due to differences in index of refraction for each color. The smaller the wavelength, the bigger the index of refraction.
Ratio of Object/Image Distance to Object/Image Height
d_o/d_i = h_o/h_i d_o: Distance Between Object and the Mirror d_i: Distance Between Image and the Mirror h_o: Height of the Object h_i: Height of the Image
Magnification for Multiple Lens System (No Contact)
m = m1 * m2 * m3 * ... * m_n
