Optical Instruments - Optics of the Eye - Long Sight or Hypermetropia - Report Writing Science Assignment Help

Assignment Task:

CHAPTER  1
OPTICS OF THE EYE

The functions of the eye

The essential function of the eye is to import to an observer knowledge about the external world. Except under conditions of extreme darkness, all objects radiate or reflect some measure of light from the visible spectrum, and it is through its sensitivity of these radiation that the eye has acquired its ability to see.

The optical system of the eye

1- Light from the external world is admitted into the interior of the eye through the cornea, a transparent segment of rather shorter radius than the rest of the eyeball.

2- The refraction which takes place at the cornea is sufficient, when combined with the additional refractive power of the crystalline lens within the eye, to focus the light onto the inner wall of the eyeball.

3- Immediately in front of the anterior surface of the crystalline lens is the iris, a fibrous membrane with a central circular aperture which contracts and expands as more or less light is incident on the eye and which to some extent compensates for sudden change in illumination level. 

4- The regions behind and in front of the crystalline lens are filled with transparent media known as the vitreous and aqueous humours respectively.

5- At the back of the eye is the sensitive surface called the retinas.  In order to see an object clearly it must be focused on this surface.  The retina is composed of a number of layers, and the back are the sensitive "seeing" elements.  

These are of two types, called rods and cones because they are found to have these shapes when examined under a microscope.  When light fails on to these receptors electrical impulses are produced which are carried along nerves to the brain.  There are numerous nerve fibbers in the eye, and they run together and connect with the brain by way of the optic nerve.

Accommodation of the eye

1- Accommodation for distances:  On looking to a near object, the eye accommodates itself by changing the power of its lens to form the image of the object on the retina.

2- Accommodation for intensity: The iris can contracts and expands as more or less light is incident on the eye and which to some extent compensates for sudden change in illumination level. 

Defects of vision

A normal eye is that which can see far objects (at infinity) distinctly, and has an amplitude of accommodation which enables it to see clearly and without strain objects as near as 25 cm from itself.   These two limits are called the normal far and near points of distinct vision.

Optical charts

The chart is drawn to a certain scale such that when placed at a distance of 6 meters from the eye to be tested, the gaps in the smallest circles subtend an angle of 1', and therefore correspond to a power of signet of 6/6.  

The circle itself has a diameter of 5' and a thickness of 1'.  The gaps in the above row subtend an angle of 1.5', and therefore correspond to a power of 6/9.  The above rows have gaps subtending angles of 2', 3', 4', 6', 10' corresponding to powers of 6/12, 6/18, 6/24, 6/36, 6/60 respectively.

The wavelength response of the eye

The eye of the standard observer is not able to detect light outside the visible spectrum.  The cornea absorbs most of the energy at wavelengths shorter than 300 Å. This causes corneal damage, and dark spectacles, which will absorb ultraviolet light, should always be worn when an ultraviolet lamp is used.  

The crystalline lens strongly absorbs radiation of wavelength below 3800 Å, and this is the minimum wavelength which can reach the retina.

CHAPTER  2
COMMON OPTICAL INSTRUMENTS

1-  The prism and grating spectrometer

The spectrometer is an optical instrument which is mainly used to study the light from different sources. As we shall see soon, it can be used to measure accurately the refractive index of glass in the form of a prism.

The instrument consists essentially of a collimator, C, a telescope, T, and a table, on which a prism PMN can be placed. The lenses in C, T are achromatic lenses. The collimator is fixed, but the table and the telescope can be rotated round a circular scale graduated in half-degrees (figure 1). 

The spectrometer is used for accurate measuring of

1- The angle A of a prism. 

2- The angle of a minimum deviation, δmin. 

The refractive index of a prism material 

The refractive index, n, of the material of  the prism can be easily calculated once A and δmin have been determined, since,

n = (sin (A + δmin) / 2) / sin A/2

 

In an experiment of this nature, the angle, A of a glass prism was found to be 59° 52', and the minimum deviation, δmin, was 40° 30'. Thus

n = (sin (59° 52' + 40° 30') / 2) / sin 59° 52'/2  = 1.539

Measurement of wavelength using a diffraction grating  

In conjunction with a spectrometer, the diffraction grating provides an easy and accurate measurement of the wavelength of light.  The grating G is placed vertically or the table and is illuminated by parallel monochromatic light.

The diffraction equation is given by d sin θ = mλ, from which knowing d and θ, the wavelength λ can he calculated.

Example 1

A parallel beam of monochromatic light is allowed to be incident normally on a plane grating having 1250 lines/cm, and a second order spectral line is observed to be deviated through 30°.  Calculate the wavelength of the spectral line?

Example 2

A grating with 8000 rulings/inch is illuminated with white light at normal incidence.  Describe the diffraction pattern assuming that the wavelength of the light extends from 4000 Å to 7000 Å

 

Example 3

A source of light emits two wavelengths, when examined with a plane diffraction grating in transmission, it is found that the spectrum of the third order of one of the wavelengths is seen in the same direction at that of the fourth order of the other wavelength.  If the difference between the two wavelengths is 1500 Å, calculate the wavelength of each spectral line?

Example 4
A plane transmission grating having 6000 lines/cm is used to obtain spectrum of light from a sodium lamp in the second order.  Calculate the angular separation between the two sodium lines whose wavelengths are 5890 and 5896 Å.

Michelson interferometer can be used to determine

1.  The wavelength of a given monochromatic light source.

2. The difference between the two neighbouring wavelengths or resolution of the spectral lines.

3.  For the measurement of the standard meter of the wavelength of light.

4.  Refractive index measurements are possible with Michelson interferometer, introducing an evacuated chamber into one beam and a chamber containing the gas or other medium into the other.

Example 1

Good fringes were observed with Michelson interferometer with monochromatic light, when the movable mirrors shifted 0.0l5 mm, a shift of 50 fringes observed.  What is the wavelength of the light used?

 

Example 2

The initial and final readings of a Michelson interferometer screw are 10.7347 mm and 10.7051 mm, as 100 fringes pass.  Calculate the wavelength of the light used?

 

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