Optics
Category : Railways
Introduction
The branch of physics which deals with the propagation, nature and behaviour of light is known as optics.
Light is a form of energy -which enables human beings and creatures to 'see' things. When light emitted from an object or reflected from the object enters our eyes we are able to see the object. We can't see an object in dark even if we are in light because there is no light coming from the object to our eyes. Light is an electromagnetic radiation which exhibits properties like a wave as well as a particle. It always propagates in a straight line. Light travels with a speed nearly equal to\[3\times {{10}^{8}}m/s\]According to current theories, no material particle can travel at a speed greater than the speed of light.
Luminous objects are those which emit its own light e.g., sun, glowworm, burning candle, electric lights. Non-luminous objects do not give out its own light but are visible only when light from a luminous object falls on it. e.g., moon, earth, table, paper, etc.
Transparent materials are those which allow most of light to pass through them. Example: Glass, water, air. Translucent materials allow only a part of light to pass through it. We cannot see distinctly through them. Example: greased paper, Paraffin wax, etc.
Opaque materials: do not allow any light to pass through it. They reflect or absorb all the light that falls on them. Example: Books, desk, stone, rubber, trees, etc.
Reflection of Light
Plane mirror is a looking glass which is highly polished on one surface and is silvered on the other surface. When a light ray strikes the polished surface, it is reflected by the silvered surface. An 'image' is defined as the impression of an object carried over and formed by light reflected from it.
(a) Plane mirrors are primarily used as looking glasses.
(b) Since, a combination of mirrors can produce multiple images, they are used to provide false dimensions in showrooms.
(c) They are also used as reflectors in solar cookers.
(d) Plane mirrors are used in the construction of a periscope.
An 'image' is defined as the impression of an object carried over and formed by light reflected from it. An image is said to be a real image if it can be caught on a screen, and a virtual image if it cannot be caught on the screen. For example, the image on the screen in a theatre is a real image and the image observed in a plane mirror is a virtual image.
(1) When the rays of light actually meet, the image so formed is known as real image.
(2) A real image can be caught on a screen since it is formed by actual meeting of rays.
(3) A real image is always inverted.
(4) A real image is formed by a convergent reflected beam.
(5) In ray diagrams, for real image, the rays are represented by full lines.
(1) When the rays of light appear to meet, the image so formed is known as virtual image.
(2) A virtual image cannot be caught on a screen since it is formed by meeting of imaginary rays.
(3) A virtual image is always erect.
(4) A virtual image is formed by a divergent reflected beam.
(5) In ray diagrams, for virtual image, the rays are generally represented by dotted lines.
The image formed by a plane mirror is
(a) Virtual (the image cannot be formed on a screen)
(b) Upright
(c) Laterally inverted (the left side of an image is formed by the right side of an object)
(d) The same size as the object
(e) The same distance behind the mirror as the object is in front of the mirror
Concave and Convex Mirror
(i) In torches, search-lights and vehicles headlights to get powerful beams of light.
(ii) As a shaving mirror to see a large image of the face.
(iii) As a dentists mirror to see large images of the teeth of patients.
(iv) Large sized concave mirror is used to concentrate sunlight to produce heat in solar furnaces.
(i) As a rear -view mirrors in vehicles.
(ii) For security purposes.
If an object is placed at a distance u from the pole of a mirror and its image is formed at a distance v (from the pole) then, \[\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\]
If a thin object linear size 0 situated vertically on the axis of a mirror at a distance u from the pole and its image of size I is formed at a distance v (from the pole), magnification (transverse) is defined as
Refraction of Light
Refractive index of medium II with respect to medium I
\[{{\mu }_{21}}=\frac{Speed\,\,of\,\,light\,\,in\,\,medium\,I}{Speed\,\,of\,\,light\,\,in\,\,medium\,II}\]
(i) Snell’s law: For any two media and for light of a given wavelength, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant. i.e., \[\frac{\sin i}{\sin r}\]=constant, where i = incidence angle, r= refraction angle.
(ii) The incident ray, the refracted ray and the normal at the incident point all lie in the same plane. When object is in denser medium and observer is in rarer medium: Refractive index \[\mu =\frac{\operatorname{Re}al\,\,depth}{Virtual\,\,depth}\]
A lens is a piece of transparent material with two refracting surfaces such that at least one is curved and refractive index of used material is different from that of the surroundings.
If an object is placed at a distance u from the optical centre of a lens and its images is formed at a distance v (from the optical centre) and focal length of this length is f then\[\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\] . This is called lens formula.
The power of a lens is defined as \[p=\frac{1}{f(in\,\,m)}\] . The unit of power is diopter.
\[\frac{1}{f}={{(}_{m}}{{\mu }_{l}}-1)\left[ \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right]\]
where\[_{m}{{\mu }_{l}}\], n refractive index of lens with respect to medium.
\[{{R}_{1}}\]= radius of curvature of first surface of lens, \[{{R}_{2}}\] = radius of curvature of second surface of lens.
When the object is placed in an optically denser medium and if the incident angle is greater than the critical angle then the ray of light gets reflected back to the originating medium. This phenomenon is called total internal reflection.
Dispersion of Light
A rainbow is a spectrum of white light from the sun. This is a phenomenon due to combined effect of dispersion, refraction and reflection of sunlight by spherical water droplets of rain.
(i) Primary rainbow: It is formed due to two refractions and one total internal reflection of the light incident on the droplet. Sunlight is first refracted as it enters a raindrop which cause different colours of light to separate. The observer sees a rainbow with red colour on the top and violet on the bottom.
(ii) Secondary rainbow: It is formed due to two refractions and two total internal reflection of light incident on the water droplet. It is due to four - step process. The intensity of light is reduced at the second reflection and hence the secondary rainbow is fainter than the primary rainbow.
As sunlight travels through the earth's atmosphere it gets scattered by the small particles present in the atmosphere. According to Rayleigh law, the amount of scattering is inversely proportional to the fourth power of the wavelength\[\left( \frac{1}{{{\lambda }^{4}}} \right)\].
(i) Blue colour of sky: Blue colour has a shorter wavelength than red colour therefore blue colour is scattered strongly. Hence the bluish colour predominates in a clear sky.
(ii) White colour of clouds: Clouds contain large dust particles, water droplets or ice particles. These large sized Particles do not obey Rayleigh law of scattering. All wavelengths are scattered nearly equally. Hence clouds are generally white.
(iii) Sun looks reddish at the Sunset or Sunrise: At sunset or sunrise, the sun's rays have to pass through a larger distance in the atmosphere. Most of the blue and other shorter wavelengths are scattered. The least scattered light reaching our eyes, therefore the sun looks reddish.
The ability of the lens to change its shape to focus near and distant objects is called accommodation. A normal human eye can see objects clearly that are between 25 cm and infinity.
Defects of Vision and Their Correction
Microscope
It is an optical instrument used to see magnified image of a tiny objects.
Resolving power of a microscope is defined as the reciprocal of the least separation between two close objects, so that they appear just separated, when seen through the microscope. Resolving power of a microscope \[\frac{1}{d}=\frac{2\mu \sin \theta }{\lambda }\]
\[\theta \] = half angle of the cone of light from the point object \[\mu \sin \theta \] = numerical aperture
It is an optical instrument used to increase the visual angle of distant large objects. It is used to see far off objects clearly.
Resolving power of telescope is defined as the reciprocal of the smallest angular separation between two distant objects, so that they appear just separated, when seen through the telescope. Resolving power of telescope \[=\frac{D}{1.22\lambda }\]
The phenomenon of redistribution of light energy in a medium due to superposition of light waves from two coherent sources is called interference of light.
(i) Two sources must be coherent.
(ii) Amplitudes of waves should be either equal or approximately equal.
(iii) Light should be monochromatic.
It is the phenomenon of restricting the vibration of light in a particular plane. Light waves are transverse in nature i.e., the electric field vector associated with light wave is always at right angles to the direction of propagation of the wave. When unpolarised light is incident on a polarized (Nicol Prism), the light wave gets linearly polarized i.e., the vibration of electric freld vector are along a single direction.
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