Optical Instruments

Optical Instruments Synopsis

Synopsis

The Human Eye

The human eye is an important and a valuable sense organ.
It is like a camera, wherein its lens system forms an image on a light-sensitive screen called the retina.
Light enters the eye through a thin membrane called the cornea. It forms a transparent bulge on the front surface of the eyeball.
The eyeball is approximately spherical in shape with a diameter of about 2.3 cm.
Most of the refraction of the light rays entering the eye occurs at the outer surface of the cornea.
The crystalline lens merely provides the finer adjustment of the focal length required to focus objects at different distances, on the retina.
We find a structure called the iris behind the cornea. The iris is a dark muscular diaphragm that controls the size of the pupil.
The pupil regulates and controls the amount of light entering the eye.
The eye lens forms an inverted real image of the object on the retina. The retina is a delicate membrane having an enormous number of light-sensitive cells. These light-sensitive cells get activated upon illumination and generate electrical signals.
These signals are sent to the brain via the optic nerves. The brain interprets these signals and processes the information because of which we can perceive the objects as they are.

Power of Accommodation

The curvature of the eye lens can be adjusted by the ciliary muscles. This changes the focal length of the lens.
The ability of the eye lens to adjust the focal length is called accommodation.
To see distant objects, the muscles relax and the lens becomes thin. This increases the focal length, thereby enabling us to see distant objects.
To see nearby objects, the muscles contract and the lens becomes thick. This decreases the focal length, thereby enabling us to see nearby objects.
The focal length cannot decrease below a minimum limit. The minimum distance at which objects can be seen most distinctly without strain is called the least distance of distinct vision. It is also called the near point of the eye.
For a young adult with normal vision, this distance is 25 cm.
The farthest point up to which the eye can see objects clearly is called the far point of the eye. It is ideally infinity for a normal eye.
The crystalline lens of people of old age becomes milky and cloudy. This condition is called cataract.
There are three refractive defects of vision caused in the human eye.

Myopia or Near-Sightedness

A person with myopia can see nearby objects clearly but cannot see distant objects distinctly.
A person with this defect has the far point nearer than infinity. Such a person may see clearly up to a distance of a few metres.
In a myopic eye, the image of a distant object is formed in front of the retina and not at the retina itself.
This defect may arise due to (i) excessive curvature of the eye lens or (ii) elongation of the eyeball.
This defect can be corrected by using a concave lens of suitable power. A concave lens of suitable power will bring the image back onto the retina and thus the defect is corrected.

Hypermetropia or Far-Sightedness

A person with hypermetropia can see distant objects clearly but cannot see nearby objects distinctly.
A person with this defect has the near point farther away from normal near point of 25 cm. Such a person has to keep the reading material farther than 25 cm.

In this case, the image of a nearby object is focused behind the retina.
This defect may arise because (i) focal length of the eye lens is too long or (ii) the eyeball has become too small.
This defect can be corrected by using a convex lens of suitable power. Eye glasses with converging lenses provide the additional focusing power required for forming the image on the retina.

Presbyopia

With age, the power of accommodation decreases. For most people, the near point gradually recedes farther away. This defect is called presbyopia.
It arises due to gradual weakening of the ciliary muscles and reducing flexibility of the eye lens.
Sometimes, a person may suffer from both myopia and hypermetropia. Such people require a bi-focal lens.
The upper part of a bi-focal lens consists of concave lens facilitating distant vision, and the lower part consists of convex lens facilitating nearby vision.

Atmospheric Refraction

Atmospheric refraction is the phenomenon of bending of light on passing through the Earth’s atmosphere. This reason for this occurrence is that the upper layers of the Earth’s atmosphere are rarer compared to the lower layers.
On account of atmospheric refraction of light,

o The stars seem higher than they actually are.

o The Sun appears to rise 2 minutes before and set 2 minutes later, increasing the apparent length of the day by 4 minutes.

o The Sun appears oval at sunrise and sunset, but appears circular at noon.

o The stars twinkle and planets do not.

Dispersion of Light

The phenomenon of splitting of white light into its constituent seven colours on passing through a glass prism is called dispersion of light.
Different colours undergo different deviations on passing through a prism.
The sequence of colours given by the prism is Violet, Indigo, Blue, Green, Yellow, Orange and Red. VIBGYOR is the acronym for this sequence.
The band of coloured components of a light beam is called its spectrum.
The red light bends the least, and the violet light bends the most.
A prism has two triangular bases and three rectangular surfaces.
Consider a light ray incident on one of its lateral surface.

Here, PE is the incident ray, EF is the refracted ray and FS is the emergent ray. A ray of light enters from air into glass at the first surface AB. The light ray on refraction bends towards the normal. At the second surface AC, the light ray enters from glass into air. Hence, it bends away from the normal.
The emergent ray is bent at an angle with the direction of the incident ray. This angle is called the angle of deviation.
If a second identical prism is placed in an inverted position with respect to the first prism, all the seven colours recombine to form white light.
A rainbow is a natural spectrum that appears in the sky after rainfall.
It is caused by dispersion of sunlight by water droplets in the atmosphere. It always forms in the direction opposite to the Sun.
The water droplets act like tiny prisms which refract and disperse sunlight. Then, they reflect light internally and refract light again.
A rainbow can also be seen on a bright sunny day if one looks through a waterfall or a fountain.

Total Internal Reflection

Critical Angle

It is the angle of incidence in the denser medium corresponding to which the angle of refraction in the rarer medium is 90°.
Consider the refraction of light from a denser medium to a rarer medium. We will consider the following three cases.

Case (i) When the angle of incidence is small, i.e., i < i_c:

A light ray AO is incident from glass at a small angle of incidence i. At the glass-air interface, it is partly reflected and partly refracted.
Since the incident ray bends away from the normal when it suffers refraction from glass to air, therefore the angle of refraction r is greater than the angle of incidence i.
Now if the angle of incidence i is increased, the angle of refraction r also increases and gradually the angle of refraction r reaches its highest value to 90° at a certain angle of incidence i which is denoted as i_c. However, the intensity of refracted keeps on decreasing.

Case (ii) When the angle of incidence is equal critical angle (i = i_c):

At a certain angle of incidence, the angle of refraction becomes 90°. The refracted ray is along the glass-air interface and is very weak. The angle ic is called critical angle.
If the angle of incidence is further increased beyond ic, i.e., i > i_c, the incident light ray OA is totally reflected and no refracted ray is obtained.

Case (iii) When the angle of incidence is greater than critical angle (i > i_c):

For the incident ray AO at an angle of incidence i greater than the critical angle ic only the reflected ray OC is obtained. In this condition, no refracted ray is obtained and the incident ray is totally reflected.

Relation between Critical angle and Refractive Index: -

Consider the refraction of a light ray at critical angle as shown in the following figure.
The refractive index of air with respect to glass is:

$begin mathsize 12px style straight mu presubscript straight g subscript straight a equals fraction numerator sin space straight i subscript straight c over denominator sin space 90 end fraction equals sin space straight i subscript straight c end style$
But, we know that

$begin mathsize 12px style straight mu presubscript straight a subscript straight g equals fraction numerator 1 over denominator straight mu presubscript straight g subscript straight a end fraction equals fraction numerator 1 over denominator sin space straight i subscript straight c end fraction equals cosec space straight i subscript straight c end style$

Factors Affecting the Critical Angle

The critical angle for a given pair of media depends on the following two factors:

Colour (or wavelength) of light: The refractive index of a transparent medium is most for violet light and least for red light, therefore the critical angle for a pair of media is least for the violet light and most for the red light. Thus critical angle increases with increase in wavelength of light.
Temperature: On increasing the temperature of medium, its refractive index decreases, so the critical angle for that pair of media increases. Thus critical angle increases with increase in temperature.

Total Internal Reflection

When a ray of light travelling in a denser medium, is incident at the surface of a rarer medium such that the angle of incidence is greater than the critical angle for the pair of media, the ray is totally reflected back into the denser medium. This phenomenon is called total internal reflection.
Thus, there are two essential conditions for total internal reflection to occur:

o The light must travel from denser to rarer medium.
o The angle of incidence must be greater than the critical angle for the given pair of media.

Scattering of Light

The phenomenon in which a part of the light incident on a particle is redirected in different directions is called scattering of light.
When the size of the scatterer (x) is very much less than the wavelength (λ) of light, Rayleigh scattering is valid. The intensity of scattered light (I_s) varies inversely as the fourth power of wavelength (λ) of incident light.

$begin mathsize 12px style straight I subscript straight s equals 1 over straight lambda to the power of 4 end style$
The phenomenon of scattering of light by colloidal particles is called the Tyndall effect.
On the basis of scattering, we can account for the: