Geometrical Optics Questions and Answers

16 Optical power also referred as dioptric power refractive power focusing power or convergence power is the degree to which a lens mirror or other optical system converges or diverges light It is equal to the reciprocal The SI unit for optical power is the inverse meter m which is commonly called the dioptre Converging lenses have positive optical power while diverging lenses have negative power When a lens is immersed in a refractive medium its optical power and focal length change of the focal length of the device i e P P High optical power Low optical power i What is the relation between the object distance u image distance v and power P in a lens a P uv u v b P c P UV V V d P U V UV UV ii Two thin lenses are kept near each other at a distance of 4 mm If the focal length of first and second lens are 20 cm and 25 cm respectively find the power of the combination a 7 6 D b 8 9 D c 7 6 D U V d 8 9 D iii A convex lens of focal length 20 cm made of glass is immersed in a liquid of refractive index 2 3 Its power will be a positive b can be positive or negative depending on the depth c zero d negative

Two converging lenses of focal lengths f and f2 are placed with their optical axes coinciding This lens system is used to form image of an object If it is found that size of the image does not depend on distance between the first lens and the object find the distance between the lenses

3 Denser medium from a rarer i i 4 Denser medium from a rarer i i A bubble in glass slab p 1 5 when viewed from one side appears at 5 cm and 2 cm from other side then thicknes of slab is 1 3 75 cm 2 23 cm 3 10 5 cm 4 1 5 cm dann end roro 3 and 4 motivaku Th

Light of wavelength 600 nm is incident on a aperture of size 2mm The distance upto which light can travel such that its spread is less than the size of aperture is NCERT Pg 379 1 12 13 m 2 6 67 m

A ray of light is incident from air on to surface of a glass medium Which of the following quantities change as the light enters the glass medium wavelength I II frequency III speed of propagation IV direction of propagation A I and III only B III and IV only C I II and IV only D I III and IV only

A lens of focal length fa in air consists of glass refractive index g If f is its focal length in a liquid refractive index then for g 1 f 0 2 f fa 3 0 f fa 4 f

40 Two identical thin plano convex glass lenses refractive index 1 5 each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the centre The intervening space is filled with oil of refractive index 1 7 The focal length of the combination is 2015 a 25 cm b 50 cm c 50 cm d 20 cm 144

42 In an astronomical telescope in normal adjustment a straight black line of lenght L is drawn on inside part of objective lens The eye piece forms a real image of this line The length of this image is 1 The magnification of the telescope is 2015 RS a L I L 1 b L I L I L

SolveLancer Test In the given figure a thin lens is made of material with u 1 5 which has one surface silve Radius of curvature of spherical surface is R What is the power of such device a Data insufficient b c NIR SolveLancer Test MIR

14 Unpolarised light surface of a material of refractive index u At a particular angle of incidence i it is found that the reflected and refracted rays are perpendicular to each other Which of the following options is correct for this situation 1 Reflected light is polarised with its electric A vector parallel to the plane of incidence 2 Reflected light is polarised with its electric vector perpendicular to the plane of incidence 3 i tan

3 An astronomical refracting telescope will have large angular magnification and high angular resolution when it has an objective lens of 1 small focal length and large diameter 2 large focal length and small diameter 3 small focal length and small diameter 11

A thin prism having refracting angle 10 is made of glass of refractive index 1 42 This prism is combined with another thin prism of glass of refractive index 1 7 This combination produces dispersion without deviation The refracting angle of second prism should be 1 6 2 8 3 10 4 4 23 The acceleration due to gravity at a height 1 km 22 ophics

An object 10 0 cm in length is placed at a di stance of 30 cm in front of a convex mirror of radius of curvature 40 cm The position o f the image its nature and size will be 2 points 30cm real 10 cm 60cm real 20 cm 45cm real 10 cm 10cm roal 15 cm

A convex mirror is dipped in a liquid whose refractive index is equal to the refractive index of material of mirror Then its focal length will Become zero O Become infinite O Remain unchanged O Become small but not zero

3 Behind a thin converging lens having both the surfaces of the same radius 10 cm a plane mirror has been placed The image of an object at a distance of 40 cm from the lens is formed at the same position What is the refractive index of the lens 1 1 5 3 9 8 0 2 5 3 4 None of these

Two transparent media of refractive indices and u have a solid lens shaped transparent material of refractive index between them as shown in figures in Column II A ray traversing these media is also shown in the figures In Column different relations between and 3 are given Match them to the ray diagra shown in Column II Match the Column I with Column II and mark the correct option from the codes given below IIT JEE 201 Column I H H i ii HI iv 14 1 H 3 H Hg P S Column II H3 H3 43 13 H3 H H H1 H1 H1 14

i The lens is thin so that the distances measured from the poles of its two surfaces can be taken as equal to the distances from its optical centre ii The aperture of the lens is small iii The object is a point object placed on the principal axis of the lens iv The incident and the refracted rays make small angles with the principal axis Let us consider a convex lens made of glass of absolute refractive index n2 placed in a rarer medium of absolute refractive index 1 Let P and P be the poles C and C the centres of curvature and R P C and R P C the radii of curvature of its first and second surfaces respectively Fig 13 Let C be the optical centre and t P P the thickness of the lens u m C K Adding Eqs i and ii we get R 1 n2 n1 V u NU Fig 13 Let a point object O be placed on the principal axis of the lens at a distance u from the pole P of the first surface A ray OA travelling in the rarer medium n is incident on the first surface of the lens It is refracted into the denser medium n along AB bending towards the normal C A N at the point A If the second surface of the lens were absent the ray AB would have met the principal axis at I which is the image of O due to refraction at the first surface Let the distance of I from P be u Then for refraction at the first surface we have 12 11 R n1 772 v t U i The ray AB travelling in medium n is actually incident on the second surface of the lens and is refracted into the rarer medium n bending away from the normal C B N at the point B The emergent ray meets the principal axis at I which is the final real image of O formed by the lens If the lens is thin then t u and can be ignored Then we have n1 122 n1 n U U R For refraction at the second surface of the lens I acts as a virtual object and I is the real image of I formed by this surface Let u be the distance of I from the pole P2 of the second surface The distance of I object for the second surface from the pole P2 of the second surface is v t Then for refraction at the second surface from denser medium 12 to rarer medium n we have 11 12 R v 11 n1 1 U u m v n v Z n 11 R2 11 12 R R ii btained by interchanging and no in the relation

a R1 As the position of an object u reflected from a concave mirror is varied the position of the image v also varies By letting the u change from 0 to infinity the graph between v versus u will be H H U 2 08 3 From NCERT 4

A capacitor of capacitance C is connected across a battery of emf E and negligible internal resistance What is the value of energy stored in between the plates of a capacitor a CE b CE C CE d 1 3 CE A convex lens is in contact ith a concave lens The magnitude of ratio of their focal length is 2 3 Their equivalent focal length is 30 cm Their individual focal length in cm are a 75 50 b 10 15 c 75 50 d 10 15

Two polaroids are placed in the path of unpolarized 16 beam of intensity I such that no light is emitted from the second polaroid If a third polaroid whose polarization axis makes an angle with the polarization axis of first polaroid is placed between these polaroids then the intensity of light emerging from the last polaroid will be 1 4 8 sin 220 Io 3 1 cos 0 COS 2 7 4 4 Incos 0 2 sin 20

2 A converging beam of rays is incident on a diverging lens Having passed through the lens the rays intersect at a point 15 cm from the lens on the opposite side If the lens is removed the point

If the angle of a wedge is 0 25 and the wavelength of sodium lines are 5890 A and 5896 A find the distance from the apex at which the maximum due to two wavelengths first coincide when observed in reflected light 3 marks

1 The frequency of a light wave in a material is 2 10 4 Hz and wavelength is 5000 A The refractive index of material will be 2007 b 3 00 d 1 40 a 1 50 c 1 33 A amall coin is resting on the bottom of a beaker

4 The value of magnification m produced by an optical device 2 What is the size and nature of an object of height 3cm 06cm virtual and erect image 03cm real and inverted image 3cm virtual and erect image 06cm real and inverted image

A point source M is placed at a distance of 30 cm from a convex lens of focal length 20 cm on its principal Axis where should a con vex mirror of focal length 15 cm be placed s o that the real image of the point source is f ormed at the source itself

An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm If the object is displaced through a distance of 20 cm towards the mirror the displacement of the image will be 1 30 cm away from the mirror 2 36 cm away from the mirror 3 36 cm towards the mirror 4 30 cm towards the mirror

Two identical equi concave lenses made of glass of refractive index 1 5 placed in contact has power P When a liquid of refractive index is filled in the gap between the concave lenses the power becomes one third of initial value The value of is 11 5 5 3 1 2

shown A ray of light makes normal incidence on the diagonal face of a right angled prism as figure If 0 37 then the angle of deviation after second step from AB is sin 37 3 5 a 53 c 106 Air B Air 5 3 90 90 C b 74 d 90

7 The diameter of the pupil of human eye is about 2 mm Human eye is most sensitive to the wavelength of 555 nm The limit of resolution of human eye is b 2 4 min a 1 2 min c 0 6 min d 0 3 min hy a distance of 0 1 mm

6 Why is the aperture of both the lenses in a microscope small OR short pulse of white light is incident from air to a glass slab at normal incidence After travell

a 5 x 10 m c 2 x 10 m 2 5 x 10 d 10 x 10 m 41 In Young s double slit experiment light waves of wavelength 5 4 x 10 nm and 68 5 x 10 nm are used in turn keeping the same geometry of the set up The ratio of the fringe widths in two cases is a 1 3 c 7 9 b 4 3 d 9 5 Intertes double 5000 was pa shifted refract a 47 In a fring dist

In the given figure the radius of curvature of curved surface for both the plano convex and plano concave lens is 10 cm 10 cm and refractive index for both is 1 5 Th location of the final image after all the refraction through lenses is a 15 cm c 25 cm b 20 cm d 40 cm

In concave mirror size of image depends upon a Size of object c Area covered by object b Position of object d Shape of object

Topic wise 5 A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm in such a way that its end closer to the pole is 20 cm away from the mirror The length of the image is 2012M b 15 cm d 5 cm a 10 cm c 2 5 cm A plano convex lens fits exactly into a plano

8 The angle of a prism is A One of its refracting surfaces is silvered Light rays falling at an angle of incidence 2A on the first surface returns back through the same path after suffering reflection at the silvered surface The refractive index the prism is a 2 sin A c 1 2 cos A b 2 cos A d tan A M of H 2014 14

A converging beam of rays is incident on a diverging lens Having passed through the lens the rays intersect at a point 15 cm from the lens on the opposite side If the lens is removed the point where the rays meet will move 5 cm closer to the lens The focal length of the lens is 2011M a 10 cm c 30 cm b 20 cm d 5 cm

50 When a biconvex lens of glass having refractive index 1 47 is dipped in a liquid it acts as a plane sheet of glass This implies that the liquid must have refractive index 2012 a equal to that of glass b less then one c greater than that of glass d less then that of glass 5

Calculate the critical angle for a ray of light passing from glycerin to water Give your answer to 1 decimal place in the form 46 4 degrees

137 If the focal length of objective lens is increased then magnefying power of 2014 a microscope will increase but that of telescope decrease b microscope and telescope both will increase c microscope and telescope both will decrease d microscope will decrease but that of taloscono increase 142

If a ray of light parallel to principle axis incident on a concave mirror at angle of incidence 37 If reflected ray meets the principle axis at point B Find distance of B from pole of mirror RED 1 3R 8 2 5R 8 3 2 4 3R 4

c 2 1 J2 The magnifying power of a telescope is 9 When it is adjusted for parallel rays the distance between the objective and eyepiece is 20 cm The focal length of lenses are 2012 a 10 cm 10 cm b c 18 cm 2 cm d 15 cm 5 cm 11 cm 9 cm

1 A ray of light is incident at an angle of incidence i on one face of prism of angle A assumed to be small and emerges normally from the opposite face If the refractive index of the prism is the tas angle of incidence i is nearly equal to 2012 a A b A 2 c A A d 2 dif is placed at

18 A convex lens of focal length 25 cm produces images of the same magnification 2 when an object is kept at two positions x and X X X from the lens The ratio of x2 and x is a 2 1 1 06 c 1 2 d 3 1

2 A concave mirror of focal length fi is placed at a distance of d from a convex lens of focal length f A beam of light coming from infinity and falling on this convex lens concave mirror combination returns to infinity 7 2012 The distance d must equal a f f c 2f f mwcl b d f f 2f f

A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length 10 cm The diameter of the Sun is 1 39 10 m and its mean distance from the earth is 1 5 10 1 m What is the diameter of the Sun s X 2008 image on the paper a 9 2 104m c 6 5 10 5 m X b 6 5 x 10 m d 12 4 x 10 4 m

A convex lens and a concave lens each having same focal length of 25 cm are put in contact to form a combination of lenses The power in diopters of the combination is 2006 a 50 c zero b infinite d 25

5 A ray of light travelling in a transparent medium of refractive index falls on a surface separating the medium from air at an angle of incidence of 45 For which of the following value of u the 105 ray can undergo total internal reflection 2010 a 1 33 b 1 40

6 5 3 3 3 23 In the shown situation if middle portion of the lens is painted black then Object Lens 2F F 5 a complete image of the object will form with low intensity b complete image of the object will form with high intensity c incomplete image of the object will form with low intensity d incomplete image of the object will form with high intensity

c 1 2 x 10 m s d 1 8 10 m s 43 Two thin lenses of focal lengths f and f are in contact and coaxial The power of the combination is 2008 a c f Vf f f 2 b d f f f f

8 A thin prism of angle 15 made of glass of mai refractive index 1 5 is combined with another prism of glass of refractive index 1 75 The xou combination of the prism produces dispersion without deviation The angle of the second prism should be 2011M a 7 c 12 b 10 d 5