Geometrical Optics Questions and Answers

p m C m D F q From the ray shown in figure we can see that n q will be a straight line Exercise In the given problem focal length of mirror is 30 em and side of square is 10 em with pP 40 cm Find perimeter of the image Ans 90 15 10 cm

56 An astronomical telescope of tenfold angular magnification has a length of 44 cm The focal length of the objective lens is a 4 cm c 40 cm b 44 cm d 440 cm DPMT 1999

For the given system if R 10 cm R 15 cm R3 15 cm The system consists of two lenses placed in contact with each other The back surface is silvered as shown R R R 3 2 Silvered surface 43 1 1 3 The equivalent focal length of system has numerical value 36 cm The equivalent focal length has numerical value 18 cm The system behaves as a concave mirror The system behaves as a convex mirror

For the given system if R 10 cm R 15 cm R 15 cm The system consists of two lenses placed in contact with each other The back surface is silvered as shown R R R WARE Silvered surface H 2 The equivalent focal length of system has numerical value 36 cm The equivalent focal length has numerical value 18 cm The system behaves as a concave mirror The system behaves as a convex mirror

An equi biconvex lens of focal length 10 cm is silvered as 3 shown in figure Refractive index of glass is equal to 2 0 Focal length of mirror silvered portion only would be equal to 5 cm Focal length of mirror silvered portion only would be equal to 2 5 cm An object is placed at point on axis such that its image is also formed at same point the distance of that point from lens would be 10 cm An object is placed at point on axis such that its image is also formed at same point the distance of that point from lens would be 5 cm

An object is placed at a distance x from a hemisphere of radius R 20 cm and 2 as shown in figure When the object is viewed from right side of the hemisphere the image appears at infinity The value of x in cm is Object X Answer R 01 02 03 04 05 06 07 08 09 00 01 02 03 04 05 06 07 8 09

The length of the side of a transparent cube is 18 cm Inside the cube there is an air bubble If it is seen from one face of the cube the depth of the bubble is 2 cm and if it is seen from the opposite face the depth is 10 cm What is the refractive index of the cube and what is the distance of the bubble from the first face 1 5 3 cm

A small lateral object initially at a distance of 30 cm start moving at t O with initial velocity 5 m s toward the pole of a silvered equiconvex lens as shown List I contains speed of image v with respect to object focal length f of the equivalent mirror magnitude only and magnification m of object 5 m s 30 cm List I I V in cm s R 10 cm II Nature of image IIIf in cm 3 2 Magnification magnitude only P 2 5 List II R let S Less than one 410 81 610 121

A hemisphere of radius 4 cm is placed centrally on a cross mark When it is viewed directly from above what will be the position of the image for the two following cases i when the plane surface of the hemisphere is in contact with the cross mark ii when the curved surface is in con tact with the cross mark i 4 cm ii 2 5 cm

4 A small fish is situated at a depth of 6 ft in a tank and at a distance of 4 5 ft from the bank A boy of height 5 ft is standing at a distance of 8 ft from the bank By what dis tance should the boy proceed towards the bank so that his movement will be visible to the fish Refractive index of water 1 33 ft 3

The length of a fish is 12 cm The fish is advancing forward to the front glass face of an aquarium When the fish is at a distance of 36 cm from the face what will be the apparent length of the fish if it is viewed through the glass face Refractive index of water relative to air 9 cm 3

3 A small electric lamp is placed at a depth of 46 cm inside a tank full of water i Calculate the area on the surface of water through which light will be emitted ii What is the maximum distance an emergent ray will travel before emerging from the surface of water of water 1 3 sin 50 3 0 7694 and tan 50 3 1 205 i 27786 4 cm ii 122 3 cm 1

A concave mirror of focal length 8 cm is placed on a table with its reflecting face turned upwards The mirror con tains a little amount of water inside it At what distance from the pole of the mirror should a point object be placed on the axis of the mirror so that the object and its image coincide Refractive index of water 12 cm

A ray of light is incident on a transparent block of refractive index 1 62 If the reflected ray and refracted ray are per pendicular to each other what is the value of the angle of incidence MPPET 02 58 3

1 ABCD is the outline of a glass cube A horizontal ray of light enters the glass cube grazing the surface AB If the ray emerges from the face BC and the ray makes an angle a with the normal at the face BC prove that sina 0 critical angle of glass C cotoc C

45 A ray of light is incident at 60 on one face of a prism of angle 30 and the emergent ray makes 30 with the incident ray The refractive index of the prism is 1 1 732 2 1 414 3 1 5 4 1 33 30 0 36

0 A part of a straight stick is immersed in water in an inclined way When the immersed portion is viewed normally from the air above it appears to be inclined at an angle of 30 with the surface of water Calculate the actual angle of the stick with the surface of water Refractive index of tan 37 6 0 77 37 6 water 4 3

Surfaces of a thin equiconvex glass lens 1 5 have radius of curvature R Paraxial rays are incident on it If the final image is formed at a R distance from the pole of the lens after n 13 internal reflections then the value of the expression n n 6 is

0 A ray of light is incident on a glass sphere and it makes an angle a with the normal and then it is refracted at an angle B Calculate the angle of deviation between the incident and emergent ray 2 B

A Initially AB is the interface of slab of refractive index u and air A ray of light strikes at AB at the critical angle C Oc Now a slab ABCD of refractive indexu is placed so that total internal reflection takes place at surface CD not at surface AB What should be the value of u 1 2 3 4 Greater than u Equal to u 8 51 Lesser than u Any value greater smaller or equal to u

cm start moving at t 0 with initial velocity 5 m s toward the pole of a silvered equiconvex lens as shown List l contains speed of image v with respect to object focal length f of the equivalent mirror magnitude only and magnification m of object 5 m s 30 cm List l V in cm s II Nature of image III f in cm H 3 2 R 10 cm OI Magnification magnitude only O1S II U III P IV R P II T III S IV R OIP II T III S IV U P 2 5 R List II S Less than one 410 81 For the shown above arrangement choose the correct option for time t 0 610 121 T Real U Virtual

A cylindrical tube filled with water 4 3 is closed at one end by silvered plano convex lens as shown in figure Refractive index of lens is 2 and radii of curvature is 5 cm A point object is placed somewhere at a point on the axis of cylindrical tube It is found that the object and image formed by L coincide with each other Then the distance of object from lens L is k cm Then value of kis D Answer 50 O 2 O 3 5 8 07 O 00 O 6

18 Light ray passes through an isosceles prism 1 5 such that the angle of incidence is equal to angle of emer gence and is th of the angle of deviation Calculate the angle of deviation HS XI 08 120 1 3

B D In a thick glass slab of thickness and refractive index n a cuboidal cavity of thickness m is carved as shown in the figure and is filled with a liquid o refractive index n2 n1 n The ratio of so that shift produced by this slab is zero when an observer A observes an object B with the paraxial rays is air air n1 n 1 1 n 11 12 n 1 n 11 1 n2 1 1 1 12 n 1 A B my

An old aged person can read the newsp aper by keeping it at 80 cm in front of hi s eye What is the nature and power of I ens required to correct the problem Al so what is the nature and power of len s required to correct the problem

1 A ray of light from air is incident on a sphere of refractive index 3 If the angle of incidence is 60 calculate the angle between the incident ray and the emergent ray with the help of a diagram 60

The image of an object placed in air formed by a convex refracting surface mathongo mathongo mathongo mothongo mathongo mathon 2nd is at a distance of 10 m behind the surface The image is real and is at 3 mathongo mathongo mathongo mathongo mathongo mathon of the distance of the object from the surface The wavelength of light mathongo mathongo mathongo mathor mathongo mathongo inside the mathon 27 mathongo mathongo surface is times the wavelength in air The mathongs mathongo mathor marzongo 24 mathon radius of the curved surface ism the value of x is mathongo mathor

43 The focal length of the objective and eye lenses of a microscope are 1 6 cm and 2 5 cm respectively The distance between the two lenses is 21 7 cm If the final image is formed at infinity what is the linear magnification a 11 c 1 1 b 110 d 44 AIIMS 2007

60 A converging simply microscope lens of focal length f is used as If the least distance of distinct vision of the observer is D and the lens is held close to the eye the magnifying power of the lens is b f D d D f a D 2 f c D 1 f IPUEE 12

33 The plane face of a planoconvex lens is silvered If u be the refractive index and R the radius of curvature of curved surface then the system will behave like a concave mirror of radius of curvature a R b c R d R 1 u 1 1 R DCE 05

41 Consider a thin prism of angle 3 and refractive index 1 5 A horizontal incident ray on prism is shown in figure If a plane mirror is vertically placed close to the prism then total deviation produced in the incident ray is 1 178 5 AT wwwwwwwww 2 177

A point source of light is placed at a depth of h below the calm surface of water From the source light rays can only be transmitted to air through a definite circu lar section i Draw the circular section of the surface of water by ray diagram and mark its radius r ii Determine the angle of incidence of a ray of light incident at any point on the circumference of the cir cular plane Given refractive index of water 3 48 36 sin 0 7501 iii Show that r h Fi 22 MESH

v u so if we put u and v for real img and real object t hen magnification should be ve Secondly if we put u and v for virtual img and real obj ect then magnification should be ve Then how come the inverse is given in the solution Pls tell where I m getting w rong 8 04 ish Mi Ask an Expert Question 20 If a lens is moved towards the object from a distance of 40 cm to 30 cm the magnification of the image remains the same numarically The focal length of the lens is 1 20 cm 2 15 cm 3 35 cm 4 18 cm Date Answer 31 01 2019 F4950 A 6018 1 1 1 Vu uf uf V u f 1 m 1 m Where m is the magnification 1 m m 1 V m V m f 40 1 1 uf f u f U u f V u U 1 40 f 2f 70 F 30 1 40 f 1 30 f As magnification is same for two object distances So it means one of the image is real and other is virtual m m For real and inverted image magnification will be negative and for virtual and erect image magnification will be positive Vo LTE 44 44 f 30 f X

A ray of light travelling through a denser medium is incident at an angle i in a rarer medium If the angle between the reflected ray and the refracted ray is 90 show that the critical angle of the two media 0c sin tani C

If the refracting angle of a prism is A the refractive index of its material is and the angle of deviation of a ray of light incident normally on the first refracting face is then prove that sin A 8 sin A

An equi biconvex lens of focal length 10 cm is silvered as shown in figure Refractive index of glass is equal to 3 NIW 2 o Focal length of mirror silvered portion only would be equal to 5 cm Focal length of mirror silvered portion only would be equal to 2 5 cm An object is placed at point on axis such that its image is also formed at same point the distance of that point from lens would be 10 cm An object is placed at point on axis such that its image is also formed at same point the distance of that point from lens would be 5

A ray of light is incident at an angle of 60 on a face of a prism with refracting angle 30 If the ray emerges from the other face and makes an angle of 30 with the incident ray then show that the emergent ray passes perpendicularly through the refracting surface Deter mine the refractive index of the material of the prism

A ray of light is incident at an angle of incidence 40 on a prism having refractive index 1 6 What should be the value of the angle of the prism for minimum deviation Given sin 40 0 6428 sin 23 42 0 4018

The refracting angle of a glass prism is 60 and the refractive index of glass is 1 6 If the angle of incidence of a ray of light on the first refracting surface is 45 Calculate the angle of deviation of the ray Given that sin 26 14 0 4419 and sin 33 46 0 555850 sin 62 47 0 8893 0 8893

2 A ray of light passes normally through a slab u 1 5 of thickness 50 mm If speed of light in vacuum be 3 x 10 m s then time taken by the ray to cross the slab will be 1 250 ps 3 250 2 5 ps 4 5

A thin lens forms image of intensity 1 If the central part of the lens of diameter half the diameter of lens is black polished then what will be the ity of image formed by the remaining part

1 A fish is a little away below the surface of a lake If the critical angle is 49 then the fish could see things above the water surface within an angular range of 0 where Air 1 Water a 0 49 0 98 90 i lie 49 b 0 90 1 d 0 24

A plane mirror is placed at a distance 12 5 cm from focus of a concave mirror of radius of curvature 20 cm Find where an object can be placed between the two mirrors so that the first image in both the mirrors coincide

2 With a concave mirror an object is placed at a distance x from the principal focus on the principal axis The image is formed at a distance x from the principal focus The focal length of the mirror is a XpX2 Jag c HE x x 2 a x x xx

A prism of refractive index 2 and apex angle A is in air as shown Light is incident from PQ side at an angle of incidence i 0 i 90 Choose the correct options R A if A 40 then light incident at all angles will be refracted at surface PR B If A 80 then light incident at some angles will be refracted and at some other angles light will be reflected at surface PR C If A 920 then light incident at all angles will be reflected at surface PR D whatever is the value of A light definitely emerge from the surface PR

A concave mirror forms the real image of an object which is magnified 4 times If object is moved 3 cm away the magnification of the image is 3 times The focal length of the mirror is Options 4 cm 3 cm 36 cm X 12 cm

c 20 cm d 45 cm a 15 cm b 30 cm A concave mirror produces a real image 1 cm tall of an object 2 5 mm tall placed 5 cm mirror the focal length of the mirror is a 4 cm b 2 cm c 12 cm d 18 cm ho pole of a converging mirror of focal leng

Q 43 Your Answer f f Option 1 f f Option 2 f f Option 3 2f f2 Option 4 2f f2 Correct Answer 2f f A concave mirror of focal length f is placed at a distance of d from a convex lens of focal length f2 A beam of light coming from infinity and falling on this convex lens concave mirror combination returns to infinity The distance d must equal Solution As we learnt in Mirror Formula 1 1 1 V U

A screen is kept at a distance of 1 m from the object A converging lens between the object and screen when placed at any two position 80 cm apart forms a sharp image of the object on the screen If the size of the object is 6 cm then gh y c azg 1 m G 42 zu la 1 Ga deg am ut gey yg ufqu a s ch gut a 80 cm Ra Rd Raau 4z zu a f da 9 qz az eur J Af Afa ga 1 uf deg si 3 6 cm ad A Focal length of lens is 9 cm 9 cm Correct Answer Your Answer The magnitude of magnification at first position when object is near to the lens is 9 Agc ad gu K 9 Correct Answer Your Answer The size of Image at second position when lens is nearer to screen than object is 54 cm 42 A c ad featu 54 cm 3 D The product of magnification m and m at two position is 1 2 3 m l quaha 1

Challenging Problem an object is placed Icm above the optical axis of a convex lens of focal length 40cm The object distan Ocm If the object now starts moving perpendicularly away from the optical axis with a speed 10 cm s peed of the image is A 5 cm s C 20 cm s D 40 cm s glob and just fail to emerge from the diage B 10 cm s