Numericals Based On Convex And Concave Mirror
1. Find the focal length of a convex mirror of radius of curvature 1m.
2. Focal length of a convex mirror is 50 cm. What is its radius of curvature?
3. Radius of curvature of a concave mirror is 25 cm. What is its focal length?
4. A concave mirror produces 10 cm long image of an object of height of 2cm. What is the magnification produced?
5. An object 1 cm high is held near a concave mirror of magnification 10. How tall will be the image?
6. An object 4 cm in size is placed at a distance of 25 cm from a concave mirror of focal length 15 cm. Find the position, nature and height of the image.
7. A converging mirror forms a real image of height 4 cm, of an object of height 1 cm placed 20 cm away from the mirror. Calculate the image distance. What is the focal length of the mirror?
8. A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification.
9. An arrow 2.5 cm high is placed at a distance of 25 cm from a diverging mirror of focal length 20 cm. Find the nature, position and size of the image formed.
10. The image formed by a convex mirror of focal length 20 cm is a quarter of the object. What is the distance of the object from the mirror?
11. Find the size, nature and position of image formed by a concave mirror, when an object of size 1 cm is placed at a distance of 15 cm. Given focal length of mirror is 10 cm.
12. An object 2cm high is placed at a distance of 16cm from a concave mirror, which produces 3cm high inverted image. What is the focal length of the mirror? Also, find the position of the image.
13. An erect image 3 times the size of the object is obtained with a concave mirror of radius of curvature 36 cm. What is the position of the object?
14. A 2.5 cm candle is placed 12 cm away from a convex mirror of focal length 30 cm. Give the location of the image and the magnification.
15. An object is placed in front of a concave mirror of focal length 20 cm. The image formed is 3 times the size of the object. Calculate two possible distances of the object from the mirror.
16. The image formed by a convex mirror is virtual, erect and smaller in size. Illustrate with figure.
17. A concave mirror produces a real image 10 mm tall, of an object 2.5 mm tall placed at 5 cm from the mirror. Calculate focal length of the mirror and the position of the image.
18. An object is placed at a large distance in front of a convex mirror of radius of curvature 40 cm. How far is the image behind the mirror?
19. An object is placed 15 cm from a convex mirror of radius of curvature 90 cm. Calculate position of the image and its magnification.
20. The image formed by a convex mirror of focal length 30cm is a quarter of the object. What is the distance of the object from the mirror?
21. When an object is placed at a distance of 60 cm from a convex mirror, the magnification produced is 1/2. Where should the object be place to get a magnification of 1/3?
22. An object is placed 18 cm front of a mirror. If the image is formed at 4 cm to the right of the mirror. Calculate its focal length. Is the mirror convex or concave? What is the nature of the image? What is the radius of curvature of the mirror?
23. A convex mirror used for rear view on an automobile has a radius of curvature of 3 m. If a bus is located at 5 m from this mirror, find the position, nature and magnification of the image.
24. An object 3 cm high is held at a distance of 50 cm from a diverging mirror of focal length 25 cm. Find the nature, position and size of the image formed.
25. An converging mirror of focal length 20 cm forms an image which is two times the size of the object. Calculate two possible distances of the object from the mirror.
26. The linear magnification of a convex mirror of focal length 15cm is 1/3. What is the distance of the object from the focus of the mirror?
27. The focal length of a convex mirror is 12.5 cm. How far is its centre of curvature (i) from the pole (ii) from the focus.
28. Find the focal length of a concave mirror that produces four times larger real image of an object held at 5 cm from the mirror.
29. An object is held at 30 cm in front of a convex mirror of focal length 15 cm. At what distance from the convex mirror should a plane mirror be held so that images in the two images coincide with each other?
30. Draw any three ray diagrams to show how the size and nature of image of an object change when it move from centre of curvature of concave mirror towards the pole of the mirror.
Numericals Based on Refraction
1. Light travels through water with a speed of 2.25 x 108 m/s. What is the refractive index of water?
2. Light travels from rarer medium 1 to a denser medium 2. The angle of incident and refraction are respectively 45° and 30°. Calculate the (i) refractive index of second medium with respect to the first medium and (ii) refractive index of medium 1 with respect to the medium 2.
3. A pond of depth 20 cm is filled with water of refractive index 4/3. Calculate apparent depth of the tank when viewed normally.
4. How much time will light take to cross 2 mm thick glass pane if refractive index of glasses is 3/2?
5. Calculate speed of light in water of refractive index 4/3.
6. A ray of light passes from air to glass (n = 1.5) at an angle of 30°. Calculate the angle of refraction.
7. A ray of light is incident on a glass slab at an angle of 45°. If refractive index of glass be 1.6, what is the angle of refraction?
8. The refractive index of diamond is 2.47 and that of glass is 1.51. How much faster does light travel in glass than in diamond?
9. The refractive index of glycerine is 1.46. What is the speed of light in air if its speed in glycerine is 2.05 x 10⁸ m/s?
10. The refractive index of glass is 1.6 and that of diamond is 2.4. Calculate (i) refractive index of diamond with respect to glass and (ii) refractive index of glass with respect to diamond.
11. A ray of light is travelling from glass to air. The angle of incidence in glass is 30° and angle of refraction in air is 60°. What is the refractive index of glass w.r.t air?
12. A ray of light is travelling from air to water. What is the angle of incidence in air, if angle of refraction in water is 45°? Take refractive index of water = 1.32
13. A water tank appears to be 4 m deep when viewed from the top. If refractive index of water is 4/3, what is the actual depth of the tank?
14. What is the real depth of a swimming pool when its bottom appears to be raised by 1m? Given refractive index of water is 4/3.
15. A jar 15 cm long is filled with a transparent liquid. When viewed from the top, its bottom appears to be 12 cm below. What is the refractive index of the liquid?
Numericals Based On Convex Lens
1. A convex lens of focal length 10 cm is placed at a distance of 12 cm from a wall. How far from the lens should an object be placed so as to form its real image on the wall?
2. If an object of 7 cm height is placed at a distance of 12 cm from a convex lens of focal length 8 cm, find the position, nature and height of the image.
3. An object 4 cm high is placed at a distance of 10cm from a convex lens of focal length 20cm. Find the position, nature and size of the image.
4. A small object is so placed in front of a convex lens of 5 cm focal length that a virtual image is formed at a distance of 25 cm. Find the magnification.
5. Find the position and nature of the image of an object 5 cm high and 10 cm in front of a convex lens of focal length 6 cm.
6. Calculate the focal length of a convex lens, which produces a virtual image at a distance of 50 cm of an object placed 20 cm in front of it.
7. An object is placed at a distance of 100 cm from a converging lens of focal length 40 cm. What is the nature and position of the image?
8. A convex lens produces an inverted image magnified three times of an object at a distance of 15 cm from it. Calculate focal length of the lens.
9. An object placed 4 cm in front of a converging lens produces a real image 12 cm from the lens. What is the magnification of the image? What is the focal length of the lens? Also draw the ray diagram to show the formation of the image.
10. A lens of focal length 20 cm is used to produce a ten times magnified image of a film slide on a screen. How far must the slide be placed from the lens?
11. Determine how far an object must be placed in front of a converging lens of focal length 10 cm in order to produce an erect image of linear magnification 4.
12. A convex lens of focal length 6 cm is held 4 cm from a newspaper, which has print 0.5 cm high. By calculation, determine the size and nature of the image produced.
13. A convex lens of focal length 0.10 m is used to form a magnified image of an object of height 5 mm placed at a distance of 0.08 m from the lens. Find the position, nature and size of the image.
14. An erect image 2 cm high is formed 12 cm from a lens, the object being 0.5 cm high. Find the focal length of the lens.
15. The filament of a lamp is 80 cm from a screen and a converging lens forms an image of it on a screen, magnified three times. Find the distance of the lens from the filament and the focal length of the lens.
16. An object 2 cm tall is placed on the axis of a convex lens of focal length 5 cm at a distance of 10 cm from the optical centre of the lens. Find the nature, position and size of the image formed. Which case of image formation by convex lenses is illustrated by this example?
17. A converging lens of focal length 5 cm is placed at a distance of 20 cm from a screen. How far from the lens should an object be placed so as to form its real image on the screen?
18. An object 5 cm high is held 25 cm away from a converging lens of focal length 10 cm. Find the position, size and nature of the image formed. Also draw the ray diagram.
19. At what distance should an object be placed from a convex lens of focal length 18 cm to obtain an image at 24 cm from it on the other side? What will be the magnification produced in this case?
20. The magnification produced by a spherical lens is +2.5. What is the nature of image and lens?
21. What is the nature of the image formed by a convex lens if the magnification produced by a convex lens is +3?
22. What is the nature of the image formed by a convex lens if the magnification produced by a convex lens is –0.5?
23. What is the position of image when an object is placed at a distance of 10cm from a convex lens of focal length 10cm?
24. Describe the nature of the image formed when an object is placed at a distance of 30 cm from a convex lens of focal length 15 cm.
25. At what distance from a converging lens of focal length 12 cm must an object be placed in order that an image of magnification 1 will be produced?
Numericals Based On Concave Lens
1. A concave lens produces an image 20cm from the lens of an object placed 30cm from the lens. Calculate the focal length of the lens.
2. The magnification of a spherical lens is +0.5. What is the nature of lens and image?
3. If an object is placed at a distance of 50 cm from a concave lens of focal length 20 cm, find the position, nature and height of the image.
4. An object is placed at a distance of 4 cm from a concave lens of focal length 12 cm. Find the position and nature of the image.
5. An object is placed at a distance of 50 cm from a concave lens produces a virtual image at a distance of 10 cm in front of the lens. Draw a diagram to show the formation of image. Calculate focal length of the lens and magnification produced.
6. A 50 cm tall object is at a very large distance from a diverging lens. A virtual, erect and diminished image of the object is formed at a distance of 20 cm in front of the lens. How much is the focal length of the lens?
7. A concave lens of focal length 15 cm forms an image 10 cm from the lens. How far is the object placed from the lens? Draw the ray diagram.
8. An object 60 cm from a lens gives a virtual image at a distance of 20 cm in front of the lens. What is the focal length of the lens? Is the lens converging or diverging? Give reasons for your answer.
9. A concave lens of 20 cm focal length forms an image 15 cm from the lens. Compute the object distance.
10. A concave lens has focal length 15 cm. At what distance should the object from the lens be placed so that it forms an image at 10 cm from the lens? Also find the magnification produced by the lens.
11. Calculate the image distance for an object of height 12 mm at a distance of 0.20 m from a concave lens of focal length 0.30m and state the nature and size of the image.
12. A concave lens has focal length of 20 cm. At what distance from the lens a 5 cm tall object be placed so that it forms an image at 15 cm from the lens? Also calculate the size of the image formed.
13. An object is placed 20cm from (a) a converging lens and (b) a diverging lens of focal length 15 cm. Calculate the image position and magnification in each case.
14. A 2.0 cm tall object is placed 40 cm from a diverging lens of focal length 15 cm. Find the position and size of the image.
15. Find the position and size of the virtual image formed when an object 2 cm tall is placed 20 cm from (a) diverging lens of focal length 40 cm and (b) converging lens of focal length 40 cm.
16. The magnification produced by a spherical lens is +0.75. What is the nature of image and lens?
17. The magnification produced by a spherical lens and a spherical mirror is +0.8. What is the nature of lens and mirror?
18. The magnification produced by a spherical lens and a spherical mirror is +2.0. What is the nature of lens and mirror?
19. The lens ‘A’ produces a magnification of –0.6 whereas lens ‘B’ produces magnification of +0.6. What is the nature of lens A and B.
20. An object is 2 m from a lens which forms an erect image one-fourth (exactly) the size of the object. Determine the focal length of the lens. What type of the lens is this?
Numericals Based On Power Of Lens
1. A concave lens produces an image 20 cm from the lens of an object placed 30 cm from the lens. Calculate the power of the lens.
2. A convex lens is of focal length 10 cm. What is its power?
3. A person having a myopia eye uses a concave lens of focal length 50cm. What is the power of the lens?
4. A thin lens has a focal length of –25 cm. What is the power of the lens and what is its nature?
5. A lens has a power of –2.5 D. What is the focal length and nature of the lens?
6. Find the power of a concave lens of focal length 2 m.
7. A convex lens forms a real and inverted image of needle at a distance of 50 cm from the lens. If the image is of the same size as the needle, where is the needle placed in front of the lens? Also, find the power of the lens.
8. Two thin lenses of power +3.5 D and –2.5 D are placed in contact. Find the power and focal length of the lens combination.
9. A doctor has prescribed a corrective lens of power –1.5 D. Find the focal length of the lens. Is the prescribed lens is diverging or converging?
10. A concave lens of focal length 25 cm and a convex lens of focal length 20 cm are placed in contact with each other. What is the power of this combination? Also, calculate focal length of the combination.
11. A convex lens of focal length 20 cm is placed in contact with a concave lens of focal length 10cm. What is the focal length and power of the combination?
12. An object is placed at a distance of 50 cm from a concave lens of focal length 30 cm. Find the nature and position of the image.
13. An object of height 2 cm is placed at a distance of 15 cm in front of a concave lens of power –10 D. Find the size of the image.
14. A convergent lens of power 8 D is combined with a divergent lens of power –10 D. Calculate focal length of the combination.
15. A concave lens is kept in contact with a convex lens of focal length 20 cm. The combination works as a converging lens of focal length 100 cm. Calculate power of concave lens.
16. Find the focal length and nature of lens which should be placed in contact with a lens of focal length 10 cm so that the power of the combination becomes 5 D.
17. A convex lens of power 3 D is held in contact with a concave lens of power –1 D. A parallel beam of light is made to fall on the combination. At what distance from the combination will the beam of light get focussed?
18. A convex lens of focal length 25 cm and a concave lens of focal length 10 cm are placed in close contact with one another. (a). What is the power of the combination? (b). What is the focal length of the combination? (c). Is this combination converging or diverging?
19. The power of a combination of two lenses X and Y is 5 D. If the focal length of lens X be 15 cm, then (a). calculate the focal length of lens Y. (b). State the nature of the lens Y.
20. Two lenses A and B have focal lengths of +20 cm and –10 cm, respectively. (a). What is the nature of lens A and lens B? (b). What is the power of lens A and lens B?