Coddington Shape Factor

Although spherical aberration cannot be eliminated for a single lens, it can be minimized by the appropriate bending of the lens into its best form. The degree of bending can be characterized by the Coddington shape factor:

R1 and R2 are the surface radii of the spherical lens surfaces.

The minimum spherical aberration also depends on the object and image distances, so another factor enters, called the Coddington position factor:

Coddington Position Factor

i and o are the image and object distances for the lens as in the lens equation.

The minimum spherical aberration occurs when

Condition for minimum spherical aberration

The higher the index of refraction n, the smaller the aberration for the optimum shape.

Lloyd's’ mirror experiment

Lloyd's mirror This is another method for finding the wavelength of light by the division of wavefront. Light from a slit So falls on a silvered surface at a very small grazing angle of incidence as shown in the diagram (Figure 1). A virtual image of So is formed at S1. Interference occurs between the direct beam from So to the observer (0) and the reflected beam The zeroth fringe will be black because of the phase change due to reflection at the surface. Application An interesting application of this effect may be observed when a helicopter flies above the sea near a radio transmitter. The helicopter will receive two signals: (a) one signal directly from the transmitter and (b) a second signal after reflection from the sea As the helicopter rises the phase difference between the two signals will alter and the helicopter will pass through regions of maxima and minima. Lloyd's mirror Experiment Lloyd’s Mirror is used to produce two-source interference...

Thin-Lens Equation:Newtonian Form

In the Newtonian form of the lens equation, the distances from the focal length points to the object and image are used rather than the distances from the lens. Newton used the "extrafocal distances" xo and xi in his formulation of the thin lens equation. It is an equivalent treatment, but the Gaussian form will be used in this resource.

Path difference and Phase difference

Path difference is the difference in path traversed by the two waves , measured in terms of wavelength of the associated wave. It has a direct relation with phase difference. Phase difference decides the nature of interference pattern but phase difference is found out by path difference. Let's assume that, two stones are thrown at two points which are very near, then you will see the following pattern as shown in the figure below: Eg: let's mark the first point of disturbance as S1S1 and the other as S2S2, then waves will be emanated as shown above. By having a cross-sectional view, you will see the same waves as shown in the figure below (in the below explanation wavelengths of waves emanated from two different disturbances is assumed to be the same). The waves emanating from S1S1 has arrived exactly one cycle earlier than the waves from S2S2. Thus, we say that, there is a path difference between the two waves of about λλ (wavelength). If the di...

Optics for Optometry

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