Light and Optics:
Light is a form of energy which travels in straight lines and causes the sensation of vision. If we interpose a small obstacle between the object and our eyes, we are unable to see it.
Composition:
In 1966, Isaac Newton passed a beam of light through a prism and found that it has seven colors, namely Violet, Indigo, Blue, Green, Yellow, Orange, Red. In these colors
Violet will have the maximum energy.
- The color of light depends on the nature of light falling on it and also on the constituent color of the incident light reflected by it.
- Violet light has nearly twice the frequency of red light and half the wavelength.
- In red light, green grass will appear black because it absorbs all colors except green and it would absorb the red rays of light falling on it.
Phenomenon of light:
Reflection:
It is the bouncing back of light rays. The simple law of reflection is that the angle between the incoming ray and the perpendicular to the surface is equal to the angle between the reflected ray and the same perpendicular.
Refraction:
It is the sudden change of direction of light when passing from one transparent substance into another. For example a ray of light passing from air into water bends
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Diffraction:
It is the spreading out of waves of light as it passes through a narrow aperture, because light is a wave of motion.
Dispersion:
When white light is passed through glass prism, it is split into the colors of the spectrum. This is because each color has its own
wavelength, which determines the angle at which light is refracted.
Scattering:
A rough surface scatters light because each part of the surface reflects the light at light at different angles which is known as scattering of light.
Absorption:
Some surfaces absorb more of the light falling on them than others. If light of all colors is absorbed, the eyes see black. A black surface absorbs more light than a white surface.
Mirrors:
Plane Mirrors work on the principle of reflection of light. When a man stands in front of a mirror, light from all parts of the body is reflected from the mirror back to the eyes and a virtual image appears to be formed behind the mirror.
Some Important Definitions:
A
Real Image is one through which the rays of light actually pass and which can be formed on a screen. A Virtual Image is one through which the rays, do not actually pass, although they appear to come from it.
Uses of Plane Mirrors:
Plane mirrors find applications in optical level, sextant, kaleidoscope,
periscope, telescope flat, dental mirror.
Uses of Concave mirrors:
These are used in reflecting
tele-scope, dental mirror, head lamp reflections, make-up mirrors.
Uses of Convex mirrors:
Safety viewers at dangerous corners, anti-shop-lifting,
car wing mirrors etc.
Curved Mirrors:
There are two types of curved mirrors used for specific purposes viz.,
concave and convex.
In Concave mirrors the light rays are reflected so as to converge to a point called the focus of the mirror.
The virtual images produced by convex mirror are erect and smaller than the object. the convex mirror is therefore used as a
rear-view mirror in vehicles as it has the advantage of a wide field of view.
Lenses:
Lenses are used in all
optical instruments, such as microscopes, telescopes, cameras, projectors.
Lenses are of two types
Convex Lens:
If a parallel beam of light is incident on a
convex lens, all rays, after passing the lens, converge on a point called the principle focus. Convex lens surfaces have a real and therefore positive radius of curvature. It has a
real and positive focal length.
Uses of Convex lenses:
Convex lenses are used as magnifying glasses, eye, glasses to correct for long sight,
microscope,
telescope objective, camera and projectors.
Concave Lens:
The rays of light spread out after passing through the lens. Concave lens surfaces have a
virtual and therefore negative radius of curvature. It has real and positive focal length.
Uses of Concave lenses:
Concave lenses are used as wide-angle
spy hole in doors, glasses to correct for short sight, wide angle lens on coach rear window, eye lens in Galilean telescope.
Power of the Lens:
The strength of a lens is described in terms of either its
focal length or its power. The power of a lens is defined as
Power of the Lens = [latex]\frac{1}{Focal\quad length\quad in\quad metres}[/latex]
According to current theories, no material particle can travel at a speed greater than the speed of light.
Luminous and Non-luminous Objects:
Luminous objects are those which emit their 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 Translucent and Opaque materials:
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.
When light hits an opaque material, the light may be absorbed by the material and converted into heat energy. If the light is not absorbed, it is bounced back or reflected at the surface of the material. The turning back of light in the same medium is called the reflection of light.
Laws of reflection
1. The angle of incidence ‘i’ is equal to the angle of reflection ‘r’.
2. At the point of incidence, the incident rays, the normal to the surface and the reflected ray all lie in the same plane.
Plane Mirrors
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.
Use of plane mirrors
(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.
Images and their properties
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 theater is a real image and the image observed in a plane mirror is a virtual image.
Real 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.
Virtual image
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.
Characteristics of images formed by a plane mirror
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 mirror :
If the reflection takes place from the inner surface of a spherical mirror, then the mirror is called concave mirror.
Uses of concave mirrors :
(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.
Convex mirror : If the outer surface of the spherical mirror acts as a reflector then the mirror is called convex mirror.
Uses of convex mirrors :
(i) As a rear -view mirrors in vehicles.
(ii) For security purposes.
Mirror Formula
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,
[latex]\frac{1}{v}[/latex]+[latex]\frac{1}{u}[/latex]=[latex]\frac{1}{f}[/latex]
Magnification
If a thin object linear size O 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
When a ray of light passes from one medium to another mediumit bends – towards the normal when goes from rarer to denser and away from the normal when goes from denser to rarer medium. This phenomenon is called refraction of light. Twinkling of stars, sun is visible to us about 2 minutes before the actual sunrise, and about 2 minutes after actual sunset etc. due to atmospheric refraction.
Refractive index
Refractive index of medium II with respect to medium I
[latex]\mu_{21}[/latex] = [latex]\frac{Speed of light in medium I}{Speed of light in medium II}[/latex]
Laws of Refraction
(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, [latex]\frac{sin i}{sin r}[/latex] = 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[latex]\mu[/latex]= [latex]\frac{Real depth}{Virtual depth}[/latex]
A lens is a piece of transparent material with two refracting surfaces such that atleast one is curved and refractive index of used material is different from that of the surroundings.
Refraction through a thin lens (lens formula)
If an object is placed at a distance u from the optical center 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
[latex]\frac{1}{v}[/latex]-[latex]\frac{1}{u}[/latex]=[latex]\frac{1}{f}[/latex]
This is called lens formula.
Power of a lens
The power of a lens is defined as
P=[latex]\frac{1}{f (in m)}[/latex]
The unit of power is diopter.
Focal length of a lens (lens maker’s formula)
R1 = radius of curvature of first surface of lens, R2 = 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.
Critical angle (ic):
When a ray passes from an optically denser medium to an optically rarer medium, the angle of refraction r is greater than the corresponding angle of incidence i. From Snell’s
law.
Critical angle
[latex](i_c)[/latex]
Let [latex]\mu_1[/latex]= [latex]\mu[/latex], [latex]\mu_2[/latex]= 1 and let i=[latex](i_c)[/latex],
r=[latex](90^0)[/latex]
then [latex]sin[/latex] [latex](i_c)[/latex] = [latex]\frac{1}{\mu}[/latex]
there fore [latex](i_c)[/latex]= [latex]sin^{-1}[/latex][latex]\frac{1}{\mu}[/latex]
[latex](i_c)[/latex] is called the critical angle.
This phenomenon takes place in shining of air bubble, sparkling of diamond, mirage, looming, in optical communication, endoscopy using optical fibre.
When a white ray of light or sunlight passes through a prism it breakes into its seven constituents colours violet, indigo, blue, green, yellow, orange and red (VIBGYOR). This phenomenon is called dispersion of light. The band of seven constituents colours is called spectrum. The deviation is maximum for violet colour and least for red colour.
The Rainbow
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. Scattering of Light 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 ([latex]λ^4[/latex])
Phenomenon based on scattering of light
(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.
Power of Accomodation of Eye:
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
Nearsightedness:
If the eyeball is too long or the lens too spherical, the image of distant objects is brought to a focus in front of the retina and is out of focus again before the light strikes the retina. Nearby objects can be seen more easily. Eyeglasses with concave lenses correct this problem by diverging the light rays before they enter the eye. Nearsightedness is called myopia.
Farsightedness:
If the eyeball is too short or the lens too flat or inflexible, the light rays entering the eye — particularly those from nearby objects— will not be brought to a focus by the time they strike the retina. Eyeglasses with convex lenses can correct the problem. Farsightedness is called hypermetropia.
Astigmatism:
Astigmatism is the most common refractive problem responsible for blurry vision. Most of the eyeball’s focusing power occurs along the front surface of the eye, involving the tear film and cornea (the clear ‘window’ along the front of the eyeball). The ideal cornea has a perfectly round surface. Anything other than perfectly round contributes to abnormal corneal curvature– this is astigmatism. Cylindrical lens is use to correct astigmatism.
It is an optical instrument used to see magnified image of a tiny objects.
Resolving power (R.P.) of a Microscope:
Resolving power (R.P.) of a microscope 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
[latex]\frac{1}{d}[/latex]= [latex]\frac{2μsinθ}{λ}[/latex]
[latex]θ[/latex]= half angle of the cone of light from the point object
[latex]μsinθ[/latex]= numerical aperture
Telescope (Astronomical)
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 (R.P.) of a telescope:
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 =[latex]\frac{D}{1.22λ}[/latex]
Interference of Light Waves:
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.
Conditions for sustained interference:
(i) Two sources must be coherent.
(ii) Amplitudes of waves should be either equal or approximately equal.
(iii) Light should be monochromatic.
Polarisation:
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 polaroid (Nicol Prism), the light wave gets linearly polarised i.e., the vibration of electric field vector are along a single direction.