Lens, magnification, optics, and a little of holographic imaging

Michael A Casciano Kotick

Starting the lectures of Physics II, nothing caught my attention more than the interesting facts about lens, and how in-depth it can be. Lens is a transparent material that is bordered with two bending planes. It will refract the light that comes from an object (Light behind an object) and makes virtual or real images of objects. Lens has two basic types, which are convex lens and concave lens. Convex lens has the thinnest part in its side, while concave lens has thinnest part in its center. The parts of a convex lens are the focus point which are principal and virtual, also principal axis, lens curvature, and optical center. Convex lens has three different shapes called: biconvex, plan-convex, and concave-convex. Although there are 3 shape of convex lens, the main system and characteristic is the same. The properties of these are collect ray which is convergent, has a positive focus value and has two focuses being principal and virtual. Particular to the ray of convex is the fact it is a ray parallel to the principal axis which is refracted through the principal focus. Also, a ray through a virtual focus is refracted parallel to the principal axis. And finally, it is a ray through the optical center that is not refracted.

Continuing, one notices the second lens called the concave lens. It is described to have the thinnest part in its center. Similar to the convex, the concave lens has three types of shapes: biconcave, plan-concave, and convex-concave. Although there are 3 shape of concave lens, the main system and characteristic is same. The concave lens has different properties being the spread ray making it divergent; it has a negative focus value, and has two focus, virtual and principal focus. Its parts consist of the optical center, focus point, principal axis and lens curvature. The particular ray is parallel to principal axis is refracted like from active focus point, F1,  yet toward F2 is refracted parallel to principal axis and finally, can be a ray through the optical center not refracted. Images on a concave lens are always makes virtual, upright, and minimized image.

The function of lens is to make optical object, like magnifying glass, eyeglasses, microscope, and others. In lens, there is also relationship between focus distance, object distance, and image distance. The formula is same with mirror:

do = Object distance to lens (m)

di = Image distance to lens (m)

f = Focus distance (m)

Beside focus, object distance, and image distance, we can calculate magnification and height of object and image.

M= Magnification

hi= Height of image

ho= Height of object

do= Object distance to lens

di= Image distance to lens 

Continuing the readings one comes across the power of lens, besides magnification and focus. Power of lens is more often used than the other. Example, you can sometimes hear in everyday life about his glasses are -1, -2, and -5. The equation has P=magnification, and f=focus distance.

The next topic is optics which is the study of the behaviour and properties of light including its interactions with matter and its detection by instruments. Optics usually describes the behaviour of visible, infrared, and ultraviolet light; however because light is an electromagnetic wave, similar phenomena occur in X-rays, microwaves, radio waves, and other forms of electromagnetic radiation and analogous phenomena occur with charged particle beams. Since the discovery by James Clerk Maxwell that light is electromagnetic radiation, optics has largely been regarded in theoretical physics as a sub-field of electromagnetism. In set theory, a branch of mathematics, a reflection principle says that it is possible to find sets that resemble the class of all sets. There are several different forms of the reflection principle depending on exactly what is meant by "resemble". In mathematics, a reflection formula or reflection relation for a function f is a relationship between f (a-x) and f(x). It is a special case of a functional equation, and it is very common in the literature to refer to use the term "functional equation" when "reflection formula" is meant. Reflection formulas are useful for numerical computation of special functions. In effect, an approximation that has greater accuracy or only converges on one side of a reflection point (typically in the positive half of the complex plane) can be employed for all arguments. The even and odd functions satisfy simple reflection relations around a=0. For all even functions,

Finally, ending with a topic that is not studied in the Physics II class but after looking up more intense information on lens, optics, and magnification, I came across the theory of holographic imaging is formulated in terms familiar from conventional optics. The effects of the curvatures and off-axis angles of the reference and read-out waves are described by equivalent thin lenses and prisms. The formation of the true-image wave field is found to be completely analogous to the conventional imaging of the object wave field by the equivalent lenses and prisms. To explain the conjugate image, we introduce the concept of time reversal. The conjugate-image wave field is the time-reversed object wave field conventionally imaged by equivalent lenses and prisms (and a plane mirror). The finite size and resolution of the photographic plate are taken into account. The size of the plate determines the effective aperture of the equivalent lenses and prisms; it is equivalent to a diaphragm in the hologram plane. The modulation transfer function of the plate has the same effect as a diaphragm inserted in the imaging bundle during the recording (or the reconstruction) with its center at the reference (read-out) point. The two diaphragms limit the field of view and the resolution. In the end, this is just a small taste of information starting from Physics II class to a more advance. Hopefully as an engineer student, I will be able to learn more about optics, lens and holographic imaging.