^Persistence of eye
Image of an object remains or persists for 0.1 s even after the object has vanished. This time is called persistence of eye.
Now if two objects are shown to eye at a time gap of less than 0.1 s, eye fails to distinguish them separately. This effect is called stroboscopic effect. Movies make use of stroboscopic effect.
^Sensitivity of human eye
The following graph shows the variation of sensitivity of human eye with the wavelength of light. From the above graph it is clear that the sensitivity of human eye is low for both red & violet colour wavelengths. It is maximum for 555 nm wavelength which corresponds to yellow – green light.
^Human eye
Eyes ball: 1 inch diameter
Cornea: Front bulged transparent, causes most of the refraction.
Eye lens: Crystalline lens hard at the middle but becomes soft towards the corners & has a average refractive index of about 1.4
Pupil: Adjustable aperture that control the amount of light entering the eye. Its size is adjusted by the iris. In ordinary light the diameter of the pupil is about 2 mm; in dim light it is about 8 mm.
Retina: It is a translucent layer at the curved back surface of the eye composed of about 125 milllion sensitive cells (optical fibers) called rods (sensitive to light) & cones (sensitive to colour) covering the curved back surface the eye & send the information of this image to brain for further processing.
Ciliary muscles: Holding eye lens & adjust the convexity of eye lens so that the near and the far objects are distinctly visible to the eye is called power of accommodation.
^Astronomical telescope
Far point case (i.e. ve → ∞), eye is least strained.
(a) 
(b) L = fo + fe = maximum (as ue = fe, when ve → ∞
^Near point case
It the object is placed between F & P of a convex lens such that the images at near point (25 cm) is formed as shown,
then the magnifying power of lens is 
Magnifying power of a simple microscope can be increased by decreasing the focal length of the lens, however generally it is not preferred, as then spherical & chromatic both defects becomes more pronounced. Also it is difficult to grind lenses of very short focal lengths. Consequently a simple microscope has a limited maximum magnification (≤ 9) for realistic focal lengths. For much larger magnifications, one uses two lenses, one compounding the effect of the other.
^Simple microscope
A simple microscope is simply a converging lens of small focal length (f < D).
Suppose a short object has a height h0 is viewed by eye without using a lens by pacing it at near point, then the visual angle made by the object eye is
Far point case
It the object is placed at F of a conves lens such that the images at far point (∞) is formed as shown,
then the magnifying power of lens 
^Spherical Aberration
Due to curvature of a lens marginal rays meet at a point situated at a nearer distance from lens & paraxial rays undergo minimum & meet at a point situated at greater distance for optical center of the lens resulting in a large no. of blurred images. It can never be eliminated but can be minimized
1. Using stops: By using stops either paraxial or marginal rays are cut off, bringing the rest practically to one focus.
However, in this method, intensity of image formed is poor.
2. Using lens of large focal length
3. Using plano-convex lens such that its curved surface faces the incident or emergent light whichever is more parallel.
^Chromatic aberration
(a) Various colors in white light get dispersed at various points on the principal axis resulting in a large no. of blurred images.
(b) Longitudinal chromatic abb. = fR – fV =df = – ωf
(c) For a combination of two lenses separated by a distance x to produce achromatism.
If lenses are in contact, then x = 0 & condition of achromatism becomes.
This is possible only if one is convex & other is concave. Also this implies ω ∝ f. In order to produce a convergent achromatic beam from a combination of a convex & concave lens in contact the lens having more focal length must have more dispersive power (more refractive index).
^Polishing lenses
When a mirror is polished it becomes a mirror of focal length ‘f’ given by 
Here f1 & f2 are the focal lengths of surfaces where a ray of light strikes for 1st & 2nd time respectively. As the ray of light strikes the 1st surface twice, hence its contribution is considered twice.
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