## Lens aberration

### Lens aberration

These are the defects in lens because of which, image formed deviates from the ideal one. They can be divided into two types:
1) Monochromatic aberration

2) Chromatic aberration.
Some of the types of monochromatic aberration are:

a) Spherical aberration

b) Coma
c) Curvature
d) Distortion

e) Astigmatism Out of these, spherical aberration is more common.

### Spherical aberration

Spherical aberration arises on account of inability of the lens to focus paraxial/central rays and marginal/peripheral rays from an object at the same point. The image of the object is, therefore, blurred. The magnitude of linear/axial spherical aberration = (fc-fm), where fc is focal length of the lens for central rays and fm is focal length of the lens for marginal rays. The linear spherical aberration is positive for a convex lens and negative for a concave lens. To remove spherical aberration, two lenses of focal lengths f1 and f2 must be separated by a distance d = f1 – f2

### Chromatic Aberration

It arises on account of inability of a lens to focus different colours of white light at the same point. Therefore, image of an object seen in white light appears coloured. The magnitude of axial chromatic aberration =(fr-fu), where fr is focal length of the lens for red light and fu is focal length of the lens for violet light.

If f =√v(fr×fu) = mean focal length of the lens, then we can show that For a convex lens, axial chromatic aberration is positive and for a concave lens, axial chromatic aberration is negative. Two lenses, one convex and the other concave of different material and suitable focal lengths can be combined to reduce chromatic aberration to zero. This combination is called an achromatic combination.
The condition for achromatism is ω1/f1+ω2/f2=0 Where f1 and f2 are focal lengths of two lenses and ω1, ω2 are the respective dispersive power of their materials. As ω1, ω2 both are positive, therefore f1 , f2 must have opposite sings to satisfy the condition for achromatism. It means one lens is convex, the other must be concave. If we have to keep the two lenses separately, then the distance d between them should be equal to average focal length of the two lenses i.e. d = ( 1 + f2)/2

### Two eye pieces

Two eye pieces in common use are -a) Huyghen’s piece and, b)Ramsden’s eye piece Both, the conditions for removal of spherical aberration and chromatic aberration are satisfied in Huyghen’s eye piece, but it cannot be used for precise measurement, because cross wires cannot be fixed. Ramsden eye piece can be used for precise measurement as cross wires can be fixed in this eye piece. However, defects of spherical aberration and chromatic aberration persist in this eye piece.

### Eye

1) Human eye resembles a photographic camera. The eye has a crystalline lens held in position by ciliary muscles, which contract or relax to change the focal length of the lens; Retina serves the purpose of film in the camera. Yellow spot is about the centre of the retina and is most sensitive to light. The point at which the optic nerve enters the eye is called blind spot. It is insensitive to light.
2) The ability of the eye to observe objects at different distance by changing the focal length of the lens is called power of accommodation.
3) The farthest point up to which the eye can see clearly is called far point of eye. The closest point up to which the eye can see clearly is called near point of the eye. The distance at which the eye can see the objects distinctly is called distance of distinct vision. For a normal eye, this distance is 25 cm.
4) The impression of an object seen by the eye persists on our mind for (1/16) second. If another object is seen before (1/16) second, the impressions of the two mix up and our eye is not able to distinguish between them. This property of human eye is called persistence of vision.

5) The seeing with two eyes is called binocular vision. It gives the three dimensional view of the objects and extends the range of vision from 3p/4 to p radian. The binocular vision also enables us to have an estimate of the distance of the objects.

### Defects of the eye

Two major defects of human eye are: Myopia or Short sightedness and Hypermeteropia or long sightedness.

### Myopia or Short sightedness

1) A myopic person can see clearly only these objects which are at short distances from the eye. This is as if far point of the eye has shifted to some nearby point.

2) This defect arises on account of elongation of eye ball or decrease in focal length of eye lens.

3) To correct this defect, the person has to wear specs using concave lens of focal length f = x = distance of far point of defective eye.

### Hypermetropia or Long sightedness

1) A hypermetropic person or a long sighted person see clearly only these objects which are at long distances, as if near point of his eye has shifted to some distant point.

2) This defect arises on account of contraction of eye ball or increase in focal length of eye lens.

3) To correct this defect, the person has to wear specs using a convex lens of focal length f given by 1/f=1/D-1/d Where d = actual distance of distinct vision of defective eye, D = distance of distinct vision of normal eye.

### Camera

In a photographic camera, following terms should be clearly understood:

1) F-numbers represent the size of aperture. Usually, f number are 2, 2.8,4, 5.6, 8, 11, 22, 32, The diameter of the aperture is given by D = f/f number. Where f is focal length of the lens.
2) The amount of light (L) entering the camera is directly proportional to area A of the aperture i.e.L ∝ A ∝d2, Where d is diameter of the aperture.
3) The brightness of image (B) is proportional to d2/ f2.

4) Exposure numbers or E-numbers marked on the lens determine time (T) of exposure. In general T ∝ 1/ (E-number).

5) The time of exposure for good quality prints depends on both f-number and E-number T ∝ {1/ (f-number)}2 ×1/ (E-number).

6) Depth of focus refers to the range of distance over which the object may lie so as to form a good quality image. Use of larger f- numbers increases depth of focus.