Optical Instruments and Photometry

1. Defects of vision:

a.The least distance upto which an object can be clearly seen by a naked eye is called the least distance of distinct vision which is 25cm for normal eye.
b.The farthest point for the clear vision is infinity.
c.Ability of eye less to change its focal length is call power of accomodation.
d.When eye is relaxed it has maximum focal length and minimum focal length when eye is most strained(25cm).
e.The limit of resolution of eye is one minute.
f.The 355 resistance of vision of human eye is (1/10) sec.

1.1. Myopia (short sightedness):
In it distant object are not clearly visible. Image of the objects from before the retina. This defect can be removed by using spectacles having divergent lens. Suppose a person can see an object at maximum (x) then to see the distant object a divergent lens has to be introduced which has a virtual image of the object at a distance of x from the eye.
   i.e. u = Infinity
     V = f = -x
     Therefore, power of the lens, P = 1/f = -(1/x)

1.2. Hypermetropia (longsightedness):
In it near objects are not clearly visible. Image of the objects form behind the retina. This deftect can be removed by using spectacles having convergent lens.
i.e. u = D
    V = -d
   Or, 1/f = 1/u + 1/V
Therefore, 1/f = 1/D - 1/d.

1.3 Presbyopia:
In this defect both near and far objects are not clearly visible. This defect takes place at old age and is called old age defect. This defect is remedied by using bifocal lens. It is due to the loss in elasticity of ciliary muscles.

1.4. Astigmatism:
It is not equally clear in two mutually perpendicular directions which is due to the uneven curvature of the cornea. This defect is corrected by using a cylindrical lens.
     Visual angle: It is the angle subtended by an object at the eye . It is maximum when the object is at the least distance of distinct vision.
     i.e. visual angle = h/D

2. Microscope:
It is an optical instrument used to increase the visual angleof near objects which are too small to be seen by our naked eye. Microscope are of two types viz, simple microscope and compound microscope.

2.1. Simple Microscope:
It is also known as magnifying glass or magnifier and consists of a convex lens with object between its focus and optical centre. The image formed by it is errect, virtual, enlarged and on the same side of lens.

2.2. Compound Microscope:
It consists of two convex lens of short focal length, objective lens and eye piece. Object is outside the focus of objective which forms real image and acts as object for the eye piece. Depending on the adjustment, the image can be formed at the least distance of distinct vision or at the infinity.

3. Telescope:
It is an optical instrument used to increase the visual angle of distant objects. They are of three types:
3.1. Astronomical telescope: It consists of two convex lens, objective lens of large focal length and aperture and eye piece of small focal length and aperture. Object is at the infinity, so the image is formed at the focus of the objective lens which acts as the object for eye piece.

3.2. Terrestrial telescope: It is used to see distant object on the earth. The final image is virtual, errect and diminished.

3.3. Galilean Telescope: It is also a type of terrestrial telescope but of much smaller field of view. It's objective lens is a convergent lens while the eye piece lens is divergent lens. The final image is virtual, errect and diminished.

4. Photometry: 
The branch of optics which study and measure the light emitting capacity of a source and illuminance produced by it.

Radiant Flux (R):
The total energy radiated by a source per second is known as Radiant Flux (R). It's unit is watt.

Luminous Flux (Ø):
The light energy radiated by a source in one second is called Luminous Flux (Ø). It's unit is lumen.

Luminous intensity (I):
The luminous flux per unit solid angle is known as Luminous intensity (I). It's unit is candela i.e, lumen per steradian.

Illuminance (E):
The luminous flux per unit area falling normally is known as Illuminance.
It's unit is lumen/m² or lux.
Therefore, E = Ø/A = I/r² (For point source)
E = Ø/A = (4(pie)I) / 2(pie)rl = 2I/rl
Therefore, E is directly porportional to 1/r ( For a cylindrical source)

Lambert Cosine Law:
It states that " at a given point for a given source illuminance varies linearly with cosine of angle of incidence ". i.e E is directly porportional to cos(theta).

Photometer: 
It is a device use to compare illuminating power of two sources.
Two sources placed at a distance r1 and r2 form a screen having same illuminance then,
E1 = E2
or, I1/r1² = I2/r2²
or, I1 /I2 = ( r1 /r2 )²