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It is used to see far off object on the earth. (1) It consists of three converging lens : objective, eye lens and erecting lens. (2) It's final image is virtual, erect and smaller. (3) Magnification : \[{{m}_{D}}=\frac{{{f}_{0}}}{{{f}_{e}}}\left( 1+\frac{{{f}_{e}}}{D} \right)\] and \[{{m}_{\infty }}=\frac{{{f}_{0}}}{{{f}_{e}}}\] (4) Length : \[{{L}_{D}}={{f}_{0}}+4f+{{u}_{e}}\] and \[{{L}_{\infty }}={{f}_{0}}+4f+{{f}_{e}}\]

By astronomical telescope heavenly bodies are seen. (1) \[{{f}_{\text{objective}}}>{{f}_{\text{eyelens}}}\]and \[{{d}_{\text{objective}}}>{{d}_{\text{eye lens}}}\]. (2) Intermediate image is real, inverted and small. (3) Final image is virtual, inverted and small. (4) Magnification :  \[{{m}_{D}}=-\frac{{{f}_{0}}}{{{f}_{e}}}\left( 1+\frac{{{f}_{e}}}{D} \right)\] and \[{{m}_{\infty }}=-\frac{{{f}_{o}}}{{{f}_{e}}}\] (5) Length : \[{{L}_{D}}={{f}_{0}}+{{u}_{e}}\] and \[{{L}_{\infty }}={{f}_{0}}+{{f}_{e}}\]

It is an optical instrument used to see very small objects. It's magnifying power is given by \[m=\frac{\text{Visual angle with instrument(}\beta \text{)}}{\text{Visual angle when object is placed at least distance of distinct vision (}\alpha \text{)}}\] (1) Simple microscope (i) It is a single convex lens of lesser focal length. (ii) Also called magnifying glass or reading lens. (iii) Magnification's, when final image is formed at D and \[\infty \] (i.e. \[{{m}_{D}}\] and \[{{m}_{\infty }}\])      \[{{m}_{D}}={{\left( 1+\frac{D}{f} \right)}_{\max }}\] and \[{{m}_{\infty }}={{\left( \frac{D}{f} \right)}_{\min }}\] (iv) If lens is kept at a distance a from the eye then \[{{m}_{D}}=1+\frac{D-a}{f}\] and \[{{m}_{\infty }}=\frac{D-a}{f}\] (2) Compound microscope (i) Consist of two converging lenses called objective and eye lens. (ii) \[{{f}_{\text{eye lens}}}>{{f}_{\text{objective}}}\]and \[{{(\text{diameter)}}_{\text{eye lens}}}>{{(\text{diameter})}_{\text{objective}}}\] (iii) Intermediate image is real and enlarged. (iv) Final image is magnified, virtual and inverted. (v) \[{{u}_{o}}=\]Distance of object from objective (o), \[{{v}_{o}}=\]Distance of image \[({A}'{B}')\] formed by objective from objective, \[{{u}_{e}}=\] Distance of \[{A}'{B}'\] from eye lens, \[{{v}_{e}}=\] Distance of final image from eye lens, \[{{f}_{o}}=\] Focal length of objective, \[{{f}_{e}}=\] Focal length of eye lens. (vi) Final image is formed at D : Magnification \[{{m}_{D}}=-\frac{{{v}_{o}}}{{{u}_{o}}}\left( 1+\frac{D}{{{f}_{e}}} \right)\] and length of the microscope tube (distance between two lenses) is \[{{L}_{D}}={{v}_{o}}+{{u}_{e}}\]. Generally object is placed very near to the principal focus of the objective hence \[{{u}_{o}}\tilde{=}\,{{f}_{o}}.\] The eye piece is also of small focal length and the image formed by the objective is also very near to the eye piece. So \[{{v}_{o}}\tilde{=}{{L}_{D}},\] the length of the tube. Hence, we can write \[{{m}_{D}}=\frac{-L}{{{f}_{o}}}\,\left( 1+\frac{D}{{{f}_{e}}} \right)\] (vii) Final image is formed at \[\infty \] : Magnification \[{{m}_{\infty }}=-\frac{{{v}_{0}}}{{{u}_{0}}}.\frac{D}{{{f}_{e}}}\]and length of tube \[{{L}_{\infty }}={{v}_{0}}+{{f}_{e}}\]   In terms of length \[{{m}_{\infty }}=\frac{({{L}_{\infty }}-{{f}_{o}}-{{f}_{e}})D}{{{f}_{o}}{{f}_{e}}}\] (viii) For large magnification of the compound microscope, both \[{{f}_{o}}\] and \[{{f}_{e}}\] should be small. (ix) If the length of the tube of microscope increases, then its magnifying power increases. (x) The magnifying power of the compound microscope may be expressed as \[M={{m}_{o}}\times {{m}_{e}}\]; where  \[{{m}_{o}}\] is the magnification of the objective and \[{{m}_{e}}\] is magnifying power of eye piece.

(1) In lens camera a converging lens of adjustable aperture is used. (2) Distance of film from lens is also adjustable. (3) In photographing an object, the image is first focused on the film by adjusting the distance between lens and film. It is called focusing. After focusing, aperture is set to a specific value and then film is exposed to light for a given time through shutter. (4) f-number : The ratio of focal length to the aperture of lens is called f-number of the camera. 2, 2.8, 4, 5.6, 8, 11, 22, 32 are the f-numbers marked on aperture. f-number \[=\frac{\text{Focal length}}{\text{Aperture}}\] \[\Rightarrow \]Aperture \[\propto \] \[\frac{1}{f\text{-number}}\] (5) Time of exposure : It is the time for which the shutter opens and light enters the camera to expose film. (i) If intensity of light is kept fixed then for proper exposure Time of exposure (t) \[\propto \frac{1}{{{\text{(Aperture)}}^{\text{2}}}}\] (ii) If aperture is kept fixed then for proper exposure Time of exposure (t) \[\propto \frac{1}{{{\text{ }\!\![\!\!\text{ Intensity}\,(I)]}^{2}}}\] \[\Rightarrow \] \[I\,t=\,\text{constant}\]\[\Rightarrow \]\[{{I}_{1}}{{t}_{1}}={{I}_{2}}{{t}_{2}}\] (iii) Smaller the f-number larger will be the aperture and lesser will be the time of exposure and faster will be the camera. (6) Depth of focus : It refers to the range of distance over which the object may lie so as to form a good quality image. Large f-number increase the depth of focus.

(1) Myopia (short sightness) : A short-sighted eye can see only nearer objects. Distant objects are not seen clearly. (i) In this defect image is formed before the retina and Far point comes closer. (ii) In this defect focal length or radii of curvature of lens reduced or power of lens increases or distance between eye lens and retina increases. (iii) This defect can be removed by using a concave lens of suitable focal length. (iv) If defected far point is at a distance d from eye then Focal length of used lens \[f=-d=-\] (defected far point) (v) A person can see upto distance \[\to x\], wants to see distance \[\to y(y>x)\] so \[f=\frac{xy}{x-y}\] or power of the lens \[P=\frac{x-y}{xy}\] (2) Hypermetropia (long sightness) : A long-sighted eye can see distant objects clearly but nearer object are not clearly visible. (i) Image formed behind the retina and near point moves away (ii) In this defect focal length or radii of curvature of lens increases or power of lens decreases or distance between eye lens and retina decreases. (iii) This defect can be removed by using a convex lens. (iv) If a person cannot see before distance  d  but wants to see the object placed at distance D from eye so \[f=\frac{dD}{d-D}\] and power of the lens \[P=\frac{d-D}{dD}\] (3) Presbyopia : In this defect both near and far objects are not clearly visible. It is an old age disease and it is due to the loosing power of accommodation. It can be removed by using bifocal lens. (4) Astigmatism : In this defect eye cannot see horizontal and vertical lines clearly, simultaneously. It is due to imperfect spherical nature of eye lens. This defect can be removed by using cylindrical lens (Torric lenses).

(1) Eye lens : Over all behaves as a convex lens of \[\mu =1.437\] (2) Retina : Real and inverted image of an object, obtained at retina, brain sense it erect. (3) Yellow spot : It is the most sensitive part, the image formed at yellow spot is brightest. (4) Blind spot : Optic nerves goes to brain through blind spot. It is not sensitive for light. (5) Ciliary muscles : Eye lens is fixed between these muscles. It's both radius of curvature can be changed by applying pressure on it through ciliary muscles. (6) Power of accomodation : The ability of eye to see near objects as well as far objects is called power of accomodation. (7) Range of vision : For healthy eye it is 25 cm (near point) to \[\infty \] (far point). A normal eye can see the objects clearly, only if they are at a distance greater than 25 cm. This distance is called Least distance of distinct vision and is represented by D. (8) Persistence of vision : Is 1/10 sec. i.e. if time interval between two consecutive light pulses is lesser than 0.1 sec., eye cannot distinguish them separately. (9) Binocular vision : The seeing with two eyes is called binocular vision. (10) Resolving limit : The minimum angular separation between two objects, so that they are just resolved is called resolving limit. For eye it is \[{{1}^{'}}={{\left( \frac{1}{60} \right)}^{o}}\].

The ordered arrangements of radiations according to wavelengths or frequencies is called Spectrum. Spectrum can be divided in two parts Emission spectrum and Absorption spectrum. (1) Emission spectrum : When light emitted by a self luminous object is dispersed by a prism to get the spectrum, the spectrum is called emission spectra. Continuous emission spectrum (i) It consists of continuously varying wavelengths in a definite wavelength range. (ii) It is produced by solids, liquids and highly compressed gases heated to high temperature. (iii) e.g. Light from the sun, filament of incandescent bulb, candle flame etc. Line emission spectrum (i) It consist of distinct bright lines. (ii) It is produced by an excited source in atomic state. (iii) e.g. Spectrum of excited helium, mercury vapours, sodium vapours or atomic hydrogen. Band emission spectrum (i) It consist of district bright bands. (ii) It is produced by an excited source in molecular state. (iii) e.g. Spectra of molecular \[{{H}_{2}},\] CO, \[N{{H}_{3}}\] etc. (2) Absorption spectrum : When white light passes through a semi-transparent solid, or liquid or gas, it's spectrum contains certain dark lines or bands, such spectrum is called absorption spectrum (of the substance through which light is passed). (i) Substances in atomic state produces line absorption spectra. Polyatomic substances such as \[{{H}_{2}},\]\[C{{O}_{2}}\] and \[KMn{{O}_{4}}\]produces band absorption spectrum. (ii) Absorption spectra of sodium vapour have two (yellow lines) wavelengths \[{{D}_{1}}(5890\,{\AA})\] and \[{{D}_{2}}(5896\,{\AA})\] (3) Fraunhoffer's lines : The central part (photosphere) of the sun is very hot and emits all possible wavelengths of the visible light. However, the outer part (chromosphere) consists of vapours of different elements. When the light emitted from the photosphere passes through the chromosphere, certain wavelengths are absorbed. Hence, in the spectrum of sunlight a large number of dark lines are seen called Fraunhoffer lines. (i) The prominent lines in the yellow part of the visible spectrum were labelled as D-lines, those in blue part as F-lines and in red part as C-line. (ii) From the study of Fraunhoffer's lines the presence of various elements in the sun's atmosphere can be identified e.g. abundance of hydrogen and helium. (iii) In the event of a solar eclipse, dark lines become bright. This is because of the reason that the presence of an opaque obstacle in between sun and earth cuts the light off from the central region (photo-sphere), while light from corner portion (cromosphere) is still being received. The bright lines appear exactly at the places where dark lines were present. (4) Spectrometer : A spectrometer is used for obtaining pure spectrum of a source in laboratory and calculation of \[\mu \] of material of prism and \[\mu \] of a transparent liquid. It consists of three parts : Collimator which provides a parallel beam of light; Prism Table for holding the prism and Telescope for observing the more...

Colour is defined as the sensation received by the eye (rod cells of the eye) due to light coming from an object. (1) Colours of opaque object : The colours of opaque bodies are due to selective reflection. e.g. (i) A rose appears red in white light because it reflects red colour and absorbs all remaining colours. (ii) When yellow light falls on a bunch of flowers, then yellow and white flowers looks yellow. Other flowers looks black. (2) Colours of transparent object : The colours of transperent bodies are due to selective transmission.. (i) A red glass appears red because it absorbs all colours, except red which it transmits. (ii) When we look on objects through a green glass or green filter then green and white objects will appear green while other black. (3) Colour of the sky : Light of shorter wavelength is scattered much more than the light of longer wavelength. Since blue colour has relatively shorter wavelength, it predominates the sky and hence sky appears bluish. (4) Colour of clouds : Large particles like water droplets and dust do not have this selective scattering power. They scatter all wavelengths alomost equally. Hence clouds appear to the white. (5) Colour triangle for spectral colours : Red, Green and blue are primary colours. (i) Complementary colours : Green and Magenta, Blue and Yellow, Red and Cyan. (ii) Combination : Green + Red + Blue = White, Blue + Yellow = White, Red + Cyan = White, Green + Magenta = White (6) Colour triangle for pigment and dyes : Red, Yellow and Blue are the primary colours. (i) Complementary colours : Yellow and Mauve, Red and Green, Blue and Orange. (ii) Combination : Yellow + Red + Blue = Black, Blue + Orange = Black, Red + Green = Black, Yellow + Mauve = Black

Rainbow is formed due to the dispersion of light suffering refraction and TIR in the droplets present in the atmosphere. Observer should stand with its back towards sun to observe rainbow. (1) Primary rainbow : (i) Two refraction and one TIR. (ii) Innermost arc is violet and outermost is red. (iii) Subtends an angle of \[{{42}^{o}}\]at the eye of the observer. (iv) More bright (2) Secondary rainbow : (i) Two refraction and two TIR. (ii) Innermost arc is red and outermost is violet. (iii) It subtends an angle of \[{{52.5}^{o}}\]at the eye. (iv) Comparatively less bright.

Molecules of a medium after absorbing incoming light radiations, emits them in all direction. This phenomenon is called Scattering. (1) According to scientist Rayleigh : Intensity of scattered light \[\propto \frac{1}{{{\lambda }^{4}}}\] (2) Some phenomenon based on scattering : (i) Sky looks blue due to scattering. (ii) At the time of sunrise or sunset sun looks reddish. (iii) Danger signals are made of red colour. (3) Elastic scattering : When the wavelength of radiation remains unchanged, the scattering is called elastic. (4) Inelastic scattering (Raman's effect) : Under specific condition, light can also suffer inelastic scattering from molecules in which it's wavelength changes.