Since focal length = focal power

RAY OPTICS PREVIOUS EAMCET BITS (ENGINEERING ). The two lenses of an achromatic doublet should have : [EAMCET 009 E] ) equal powers ) equal dispersive powers ) equal ratio of their power and dispersive power 4) sum of the products of their power and dispersive power should be equal to zero Ans : 4 ω ω Sol. The condition for an achromatic doublet is + 0 ωp+ ωp 0 f f Since focal length focal power. Statement (S) : Using Huygen s eye piece measurements can be taken but tare not correct Reason (R) : The cross wires, scale and final image are not magnified proportionately because the image of the object is magnified by two lenses, whereas the cross wire scale is magnified by one lens only. Identify the correct one of the following : [EAMCET 008 E] ) Both S and R are true, R explains S ) Both S and R are true but R cannot explain S ) only S is correct, but R is wrong 4) Both S and R are wrong Ans : Sol. Huygen eye piece is not mainly used for measurement. Therefore both statement and Reason are correct.. The refractive index of a material of a plano concave lens is 5/, the radius of curvature is 0.m. The focal length of the lens in air is [EAMCET 008 E] ) 0.45m ) 0.6 m ) 0.75 m 4).0 m Sol. From lens makers formula, for plano concave lens ( μ ) F R 5 F 0. F 0.45 m 4. An achromatic combination of lenses produces [EAMCET 008 E] ) Images in black and white ) Coloured images ) Images unaffected by variation of refractive index with wave length 4) Highly enlarged images are formed Sol. Images in Achromatic Combination of lens are independent of variation of refractive index with wavelength. 5. Match the following : [EAMCET 007 E] List I List II ) Burning candle i) Line spectrum

) Sodium vapour ii) Continuous spectrum ) Bunsen flame iii) Band spectrum 4) Dark lines in solar spectrum iv) Absorption spectrum ) iii, i, ii,4 iv ) iii, ii, i,4 iv ) ii, ii, i,4 iv 4) ii, i, iii,4 iv Sol. ) Burning candle, incandescent lamp are the examples of continuos spectrum ) Sodium vapour is example of line spectrum ) Bunsen flame is example of band spectrum 4) Dark lines in solar spectrum called as Fraunhoffer lines are due to absorption spectrum. 6. The refractive index of the material of a double convex lens is.5 and its focal length is 5 cm. If the radius of curvature ar equal, the value of the radius of curvature (in cm) is [EAMCET 007E] ) 5.0 ) 6.5 ) 8.0 4) 9.5 Sol. The lens makers formula for thin lens is ( μ ) + F R R But given R R R [double convex] (.5 ) R 5cm 5 R 7. In Ramsden eyepiece, the two planoconvex lenses each of focal length f are separated by a distance cm. The equivalent focal length (in cm) of the eyepiece [EAMCET 007 E] ) 0.5 ).0 ).5 4) 5.5 Ans : f d Sol. The distance between two plano convex lens in Ramsden eye piece is d f f 8 cm Equivalent focal length of the eye piece f.5cm 4 8. In Huygen s eyepiece ) The cross wires are outside the eye piece ) Condition for achromoatism is satisfied ) Condition for minimum spherical aberration is not satisfied 4) The image formed by the objective is a virtual image Sol: In Huygens eyepiece both spherical an chromatic aberration are eliminated, since the distance between the lenses is f. 9. The two surfaces of a biconvex lens has same radii of curvatures. This lens is made of glass of refractive index.5 and has a focal length 0 cm in air. The lens is cut into two equal halves along a plane perpendicular to its principal axis to yield two planoconvex lenses. The two pieces are glued such that the convex surface touch each other. If this combination lens is immersed in water (refractive index 4/), its focal length (in cm) is [EAMCET 006 E] ) 5 ) 0 ) 0 4) 40

Sol. Let F is the focal length of a biconvex lens, if the lens is cut into two equal parts to yield two plano-convex lenses then the focal length of two parts is F each. When they are kept in contact, then effective focal length of combination is + + f f f F F F f F (i.e) no change in focal length let F ω is the focal length of lens in water ( μg ) + () Fair R R μg +..() Fwater μω R R Dividing () and () 4 F μω μg ω 4 Fa ( μg μ ) 4 ω F water 4 x 0 40 cm 0. Dispersive power depends on the following: [EAMCET 006 E ] ) material of the prism ) shape of the prism ) size of the prism 4) size, shape and material of the prism Sol. Dispersive power is the characteristic property of material. Therefore it depends on the material of prism. Match the appropriate pairs from Lists I and II [EAMCET 006 E ] List I List - II a) Nitrogen molecules e) Continuous spectrum b) Incandescent solids f) Absorption spectrum c) Fraunhofer lines g) Band spectrum d) Electric arc between iron rods h) Emission spectrum ) a g,b e,c f,d h ) a f,b e,c h,d g ) a h,b e,c f,d g 4) a e,b g,c h,d f Sol.. Assertion (A) : Propagation of light through an optical fibre is due to total internal reflection taking place at the core-clad interface. Reason (R ) : Refractive index of the material of the core of the optical fibre is greater than that of air. [EAMCET 005 E ] ) Both A and R are true and R is the correct explanation of A ) Both A and R are true and R is not the correct explanation of A ) A is true but R is false 4) A is false but R is true Sol. The condition for total internal reflection which takes place in optical fibre is due to i) Light travels from denser medium to rarer medium ii) Angle of incidence should be greater than critical angle

. The focal length of an equi-convex lens is greater than the radius of curvature of any of the surfaces. Then the refractive index of the material of the lens is [EAMCET 005 E] ) greater than zero but less than.5 ) greater than.5 but less than.0 ) greater than.0 but less than.5 4) greater than.5 but less than.0 Sol. Lens makers formula for equi-convex lens is ( μ ) F R R F [ μ ] If F < R, So ( μ ) < Therefore ( μ ) < or μ<.5 As focal length of convex lens is positive. So, μ cannot be negative, hence μ should be greater than zero but less than.5 4. Fraunhoffer lines are produced by the absorption of light in [EAMCET 005 E] ) The chromosphere of the Sun ) The photosphere of the Sun ) The atmosphere of the Earth 4) The ionosphere of the Earth Sol. Fraunhoffer lines are produced by the absorption of light in the chromosphere of sun. 5. Assertion (A) : Optical fibres are widely used in communication network. Reason (R ) : Optical fibres are small in size, light weight, flexible and there is no scope for interference in them. [EAMCET 004 E] ) Both A and R are true and R is the correct explanation of A ) Both A and R are true and R is not the correct explanation of A ) A is true but R is false 4) A is false but R is true Sol. Optical fibres are used in communication network because there is no loss of energy 6. The refraction angle of a prism is A and the refractive index of the material of the prism is cot(a/). The angle of minimum deviation of the prism is : [EAMCET 004 E] ) π+ A ) π A ) A A+ d sin Sol. From Snells law μ A sin A But given that μ cot A+ d A A+ d sin cos sin A cot (or) A A A sin sin sin π π + 4) A 4

A A+ d A A+ d (or) sin 90 sin (or) 90 d 80 A 7. The principal section of a glass prism is an isosceles triangle ABC will AB AC. The face AC is silvered. A ray of light is incident normally on the face AB and after two reflections, it emerges from the base BC perpendicular to the base. Angule BAC of the prism is [EAMCET 004 E] ) 0 ) 6 ) 60 A 4) 7 Sol. From the figure i 90 ( 90 A) A and α 90 i 90 A α i i i 90 α 90 ( 90 A) A i β 90 i 90 A i From the geometry of the figure A+ A+ A 80 β A 6 B C 8. A ray of light is incident on the hypotenuse of a right-angled prism after travelling parallel to the base inside the prism. If μ is the refractive index of the material of the prism, the maximum value of the base angle for which light is totally reflected from the hypotenuse is [EAMCET 00 E] ) sin ) tan μ ) sin 4) cos μ μ μ μ A Sol. Angle made by the emergent ray RS with base is BC or QR 90 - C R But μ Incident Q sin c cos( 90 c) cos θ ray C cos θ P μ θ90-c Base θ cos μ S B C Emergent ray 9. A prism of refractive index μ and angle A is placed in the minimum deviation position. If the angle of minimum deviation is A, then the value of A in terms of μ is [EAMCET 00 E] ) cos ( μ ) ) sin μ μ ( μ ) ) cos 4) sin From Snell s law in the minimum deviation position for prism A+ d sin μ A sin given that d A 5

on simplifying A+ A A A sin sin cos sin A μ A A A sin sin sin A μ cos μ A cos 0. A convex lens of focal length 0.5 m is made of a material of refractive index /. When it is placed in a liquid, its focal length is increased by 0.5m. The refractive index of the liquid is [EAMCET 00 E] ) 7 4 ) 5 4 ) 9 4 4) Sol: We know f f liq air ( μg ) μ ( g ) μ μ ( / ) μ ( μ ) 0.5 + 0.5 0.5 / 5 Solving the above equation, we get μ 4. A prism is made up of material of refractive index. The angle of the prism is A. If the angle of minimum deviation is equal to the angle of the prism, then the value of A is [EAMCET 00 E] ) 0 ) 45 ) 60 4) 75 Sol: A+ D sin m μ sin ( A / ) But A D m ( given) sina sina/cosa/ μ sin ( A / ) sin A / μ cosa/ cos A / / A/ 0 A 60. In the visible region the dispersive powers and the mean angular deviations for crown and flint glass prism ωω, are d,d respectively. The condition for getting dispersion with zero deviation, when the two prisms are combined is [EAMCET 00 E] ) ω d + ω d 0 ) ω d +ω, d 0 ) ω d+ω d 0 4) ( ω d) + ( ω d ) 0 6

Sol: The condition for getting dispersion without deviation when two prisms are combined is ω d+ω d 0 which is called as condition for achromatism. One face of the glass prism is silver polished. A light ray falls at an angle of 45 on the other face. After reflection it is subsequently reflected from the silvered face and then retraces its path. The refracting angle of the prism is 0. The refractive index of the prism is [00 E] ) ) ) 4) Sol: Angle of incidence (i) 45 r+ r A 0 sin i μ [ from Snell s law] sin r When the ray of light retraces its path at the silvered face, the angle of refraction becomes 0. sin i / μ sin r / 4. When a glass prism of refracting angle 60 is immersed in a liquid its angle of minimum deviation is 0. The critical angle of glass with respect to the liquid medium is [00 E] ) 4 ) 45 ) 50 4) 5 Sol: We know A 60 and D m 0 If C is critical angle then μ we know that μ sin c sin C C 45 μ 5. In a compound microscope crosswires are fixed at the point : [EAMCET 000E] ) Where the image is formed by the objective ) Where the image is formed by the eye piece ) Where the focal point of the objective lies 4) Where the focal point of the eye-piece lies Sol: Crosswires in a compound microscope are fixed at the same point where the image due to the objective is formed. 6. Consider the following two statements A and B identify the correct choice in the given answer A: Line spectra is due to atoms in gaseous state B : Band spectra is due to molecules. [EAMCET 000 E] ) Both A and B are false ) A is true and B is false ) A is false and B is true 4) Both A and B are true Sol: Band spectrum is formed by gases which are in molecular state. It is also called as molecular spectrum. Line spectrum is formed by gases which are in atomic state. It is also called as atomic spectrum. 7. Under minimum deviation condition in a prism, if a ray is incident at an angle 0, the angle between the emergent ray and the second refracting surface of the prism is : (Angle of the prism 60 ) [EAMCET 000 E] ) 0 60 ) 0 i0 e 7 60

) 45 4) 60 Ray Optics Sol: At minimum deviation position of a prism, angle of incidence and angle of emergence are equal. i e 0 The angle between the emergent ray and the second refracting surface will be 90 e 90 0 60 8. The focal length of the lenses of an astronomical telescope are 50 cm and 5 cm. The length of the telescope when the image is formed at the least distance of distinct vision is [EAMCET 000E] ) 45 cm ) 55 cm ) 75/6 m 4) 5/6 cm Sol: f 0 50 cm f e 5 cm When the final image is formed at least distance of distinct vision, it length L f0 + ue vf e e ( 5)( 5) 5 But u e cm ve + fe ( 0) 6 5 5 L 50+ cm 6 6 MEDICAL 9. A glass slab of thickness 8 cms contains the same number of waves as 0 cm long path of water when both are traversed by the same monochromatic light. If the refractive index of water is 4/., the refractive index of glass is : [EAMCET 009 M] ) 5 ) 5 ) 6 4 5 4) Sol: ( μ glass )( 8) ( μ water )( 0) 4 0 5 μ glass 8 0. In Huygen eye piece [EAMCET 008 M] ) Chromatic aberration is not eliminated ) Spherical aberration is completely eliminated ) Focal length of field lens and eye lens are equal 4) Cross wires cannot be provided Sol. In Huygens eyepiece spherical aberration and chromatic aberration are completely eliminated because both the conditions to eliminate them are satisfied. Solar spectrum is an example of [EAMCET 008 M] ) line emission spectrum ) band absorption spectrum ) line absorption spectrum 4) continuous emission spectrum Sol. Solar spectrum is an example of line absorption spectrum since dark lines are observed. In Ramsden s eyepiece the focal length of each lens is F. The distance of the image formed by the objective lens from the eye lens is [EAMCET 007 M] 8

) 4F 5 ) F 4 ) F Sol. The distance of image formed by the object lens from the eye lens 4) F F F F + 4 Ray Optics. 8 The velocities of light in two different mediums are 0 ms 8 and.5 0 ms respectively. The critical angle for these medium is [EAMCET 007 M] 4 ) sin ) sin ) sin 4) sin 5 5 4 Sol. If c is the critical angle velocity of light in medium sin c velocity of light in vaccum velocity of light in denser medium velocity of light in rarer medium 8 0 4 sin c 8.5 0 5 4 c sin 5 4. A diverging meniscus lens of.5 refractive index has concave surfaces of radii and 4 cm. The position of the image if an object is placed cm in front of the lens is [EAMCET 007 M] ) 7 cm ) 8 cm ) 9 cm 4) 0 cm Sol. Lens makers formula for a lens is ( μ ) F R R R cm, R 4 cm ( μ ) (.5 ) F + + 4 4.() from u, v formula + +.. () F u v F v comparing () and () (.5 ) + + 4 v on solving v -8 cm 5. In Ramsden s eye piece, the two plano convex lenses each of focal length f, are separated by a distance cm. The equivalent focal length (in cm ) of the eye lens [EAMCET 007 M] ) 0.5 ) ).5 4) 5.5 Sol. The distance between two plano-convex lenses in Ramsden s eyepiece is f d f 8cm 9

0 Ray Optics Equivalent focal length in Ramsdens eyepiece is f 8.5cm 4 4 6. A light ray is travelling between two media as given below. The angle of incidence on the boundary in all the cases is 0. Identify the correct sequence of increasing order of angles of refraction [EAMCET 006 M] ) a, b, c ) b, c, a ) c, a, b 4) a, c, b sin i sin i Sol. From Snell s law μ sin r sin r μ As i is constant sin r μ μ ω 4 ) air to water μ μa μ g / 9 ) water to glass μ μω 4/ 8 μ ω 4/ 8 ) glass of water μ μg / 9 As μ >μ >μ sinr < sinr < sinr Increasing order is a, b, c 7. The effective focal length of the lens combination shown in figure is 60 cm. The radii of curvature of the curved surfaces of the plano-convex lenses are cm each and refractive index of the material of the lens is.5. The refractive index of the liquid is [EAMCET 006 M] ). ).4 ).5 4).60 Ans; 4 Sol. The given figure is When lens are kept in contact + + () F f f f from lens makers formula ( μ ) (.5 ) f R R f..() f 4 ( μ ) ( μ ) () f 6 (.5 ) (4) f 4 Also F - 60 cm.(5) from (), (), (), (4), (5) ( μ ) + 60 4 6 4 On solving μ.6

8. A combination of two thin lenses of the same material with focal lengths f and f, arranged on a common axis minimizes chromatic aberration, if the distance between them is [EAMCET 005 M] ) ( f ) + f ) ( ) + f ) ( f+ f) 4) f ( + f) 4 f+ f Sol. The condition for minimizing chromatic observation is the distance between them is 9. If the focal length of a double convex lens for red light is f R, its focal length for the violet light is [EAMCET 005 M] ) f R ) greater than f R ) less than f R 4) f R Sol. From lens makers formula ( μ ) F R R As μ V >μ R FR > FV since < ( μ ) F Focal length for the violet light is less than for red light 40. A thin equiconvex lens is made of glass of refractive index.5 and its focal length is 0.m. If it acts as a concave lens of 0.5 m focal length when dipped in a liquid, the refractive index of liquid is [EAMCET 005 M] ) 7 8 ) 5 8 ) 8 4) 9 8 μg +..() Fair R R μg + () Fliq μ R R dividing () and () F ( μ liq g ) μ F μ μ Sol. ( ) air ( g ) (.5 ) ( μ ) 0.5 μ 0..5 7.5 5 on solving μ 4 8 4. A thin converging lens is made up of glass of refractive index.5. It acts like a concave lens of focal length 50 cm., when immersed in a liquid of refractive index 5/8. The focal length of the converging lens in air is, in metres [EAMCET 004 M] ) 0.5 ) 0.0 ) 0.5 4) 0.40 Sol. From lens makers formula

( μg ) +...() Fair R R μg μ +...() Fliquid μ R R glass and liquid dividing () and () F ( μg liq ) μ Fair ( μ g μ ) [- ve sign because of concave nature] 50 (.5 ) 5 / 8 Fair (.5 5/8) on solving F air 0. m 4. The phenomenon used in optical fibres for transmission of light energy is [EAMCET 004 M] ) Total internal reflection ) Scattering ) Diffraction 4) Refraction Sol. Total internal reflection so that no loss of energy takes place during transmission of light energy. 4. In Foucault s rotating mirror experiment to determine the velocity of light in air, the distance of the rotating mirror from the concave mirror is 6000 metres. The reflected ray is displaced through an angle of 48π 0 8 radians. If the velocity of light in air is 0 m/s, the number of rotations made by the rotating mirror in one minute are [EAMCET 00 M] ),000 ) 9,000 ) 8,000 4)6,000 Sol. Velocity of light in air 4πnd θ cθ n number of rotations 4 π d 8 Given c 0 ms, θ 48π 0 rad d distance of rotating mirror from 6000 m concave mirror on substituting in above equation n 00 turns / s 800 turns/ min 44. One of the refracting surface of a prism of the refractive index is silvered. The angle of the prism is equal to the critical angle of a medium of refractive index. A ray of light incident on the unsilvered surface passes through the prism and retraces its path after reflection at the silvered face. Then the angle of incidence on the unsilvered surface is [EAMCET 00 M] ) 0 ) 0 ) 45 4) 60

Sol. Given that A C μ sin c sin c μ A C A 0 angle of refraction 0 r sin i μ sin i i 45 sin r 45. A ray of light is incident at 60 on prism of refracting angle 0. The emerging ray is at an angle 0 with the incident ray. The value of refractive index of the prism is [EAMCET 00 M] ) ) 4 ) 4) Sol. Angle of prism 0 A Angle of incidence i 60 Angle of emergence i? Angle of deviation D 0 i A + D i 0 + 0 60 0 r 0 r A-r 0 0 0 sin ii sin 60 μ sin r sin 0 46. The focal length of biconvex lens of refractive index / is 40 cm. Its focal length in meters, when immersed in a liquid of refractive index 4/ is [EAMCET 00 M] ) 60 ) 6 ).6 4) 0.5 Sol. ( μg ) +...() Fair R R μg μ +...() Fliq μ R R dividing () and () 4 Fliq ( μg ) μ 4 Fair ( μg μ ) 4 fliq 4fair 4( 40).6m 47. A converging crown glass lens has a focal length 0 cm for the violet rays. Its focal lengths for red rays is (given μ r.5, μ v.56 ) [EAMCET 00 M] ) 0.8 cm ). cm ).85 cm 4) 4.85cm ( μ ) + fα f R R μ fred μv.54 f μ.5 violet R

0.54 fred 0 0.76cm 0.5 48. Consider the following two statements A and B, and identify the correct choice in the given answer. [EAMCET 00 M] A : In Huygens eyepiece, the two plane surfaces of two planoconvex lenses face towards the eye. B: In Huygens eyepiece the focal length of the field lens is equal to the focal lengthy of eye lens. ) Both A and B are true ) A is true but B is false ) A is false but B is true 4) Both A and B are false Sol. In Huygen s eyepiece, the two plane surface of two plano convex lenses face towards the eye. But the focal length of the field lens is thrice to the focal length of eye lens 49. Fraunhofer lines are due to [EAMCET 00 M] ) the diffraction effects in the atmosphere ) the absorption of Sun s radiation by the earth s atmosphere ) the absorption of Sun s radiation by the Sun s atmosphere 4) the characteristic emission of Sun s radiation Sol. Dark lines observed in the solar spectrum due to absorption of suns radiation by the suns atmosphere. 50. When a ray of light is incident normally on one refracting surface of an equilateral prism [Refractive index of the material of the prism is.5] [EAMCET 000 M] ) Emerging ray is deviated by 0 ) Emerging ray is deviated by 45 ) Emerging ray just grazes the second refracting surface 4) The ray undergoes total internal reflection at the second refracting surface Sol: Angle of the prism 60 A Refractive index.5 Angle of incidence at the st face AB 0 Angle of incidence at the nd face AC is 60 which is 60 greater than the critical angle of glass (4 ). Therefore total internal reflection takes place. B C 5. In Focault s rotating mirror experiment for determining the velocity of light. The distance between the rotating mirror and convex lens is negligible. When compared to the radius of curvature of the concave mirror. If the radius of curvature of the concave mirror is doubled, the image shift is [EAMCET 00 M] ) halved ) doubled ) zero 4) independent of radius of curvature of concave mirror 8πnad Sol: Velocity of light C ( b + d) x As b < d, b can be neglected 8πnad x x d ( d)( c) As d is doubled, image shift also will be doubled. 4

5. Consider the following two statements A and B and identify the correct choice in the given answer: [EAMCET 000 M] A : The curved surfaces of Plano convex lenses in Ramsden s eye piece face each other. B: The focal length of the field lens is three times the focal length of eye lens in Ramsden s piece ) Both A and B are true ) Both A and B are false ) A is true and B is false 4) A is false and B is true Sol: In Ramsden s eye-piece, focal lengths of field lens and eye-lens are equal. 5. In a compound microscope the focal lengths of two lenses are.5 cm and 6.5 cm. If an object is placed at cm from objective and the final image is formed at 5 cm from eye lens, the distance between the two lenses is [EAMCET 000 M] ) 6.00 cm ) 7.75 cm ) 9.5 cm 4).00 cm Ans:4 Sol: f 0.5 m focal length of objective f e 6.5 cm focal length of eye piece u0 cm and ve D 5cm uf 0 0 image distance from the objective V 0 u0 f0 6cm vf e e Object distance from the eye-piece u e ve fe 5cm Length of the microscope v0 + ue 6+ 5 cm 5