Question 46:
A lens of focal length 12 cm forms an erect image three times the size of the object. The distance between the object and image is :
(a) 8 cm (b) 16 cm (c) 24 cm (d) 36 cm
Solution : Question 47:
If an object is placed 21 cm from a converging lens, the image formed is slightly smaller than the object. If the object is placed 19 cm from the lens, the image formed is slightly larger than the object. The approximate focal length of the lens is :
(a) 5 cm (b) 10 cm (c) 18 cm (d) 20 cm
Solution :
(b) 10 cm
The image is slightly smaller than the object when the object lies beyond 2f; and the image is slightly larger than the object when the object between f and 2f. This means that between 21 cm and 19 cm lies 2f. Out of the given options, 20 cm lies between 21 cm and 19 cm.
So, 2f = 20 cm.
f = 10 cm.

Question 48:
An object is placed at the following distances from a convex lens of focal length 15 cm :
(a) 35 cm (b) 30 cm (c) 20 cm (d) 10 cm
Which position of the object will produce :
(i) a magnified real image ?
(ii) a magnified virtual image ?
(iii) a diminished real image ?
(iv) an image of same size as the object ?
Solution :
Here, f=15cm and 2f=30cm
(i) 20 cm (Because a magnified real image is formed when the object is placed between f and 2f).
(ii) 10cm (Because a magnified virtual image is formed when the object is placed between f and the lens).
(iii) 35cm (Because a diminished real image is formed when the object is placed beyonf 2f).
(iv) 30cm (Because an image of same size as the object is formed when the object is placed at 2f).

Question 49:
When an object is placed at a distance of 36 cm from a convex lens, an image of the same size as the object is formed. What will be the nature of image formed when the object is placed at a distance of:
(a) 10 cm from the lens ? (b) 20 cm from the lens ?
Solution :
Here, 2f = 36 cm, f = 18 cm.
(a) When the object is placed at a distance of 10 cm from the lens, the object lies within the focus. Hence, the image formed is virtual, erect and magnified.
(b) When the object is placed at a distance of 20 cm from the lens, the object lies between f and 2f. Hence, the image formed is real, inverted and magnified.

Question 7:
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 ?
Solution : Question 8:
State and explain the New Cartesian Sign Convention for spherical lenses.
Solution :
New Cartesian Sign Convention for spherical lenses:
(i) All the distances are measured from the optical centre of the lens.
(ii) The distances measured in the same direction as that of incident light are taken as positive.
(iii) The distances measured against the direction of incident light are taken as negative.
(iv) The distances measured upward and perpendicular to the principal axis are taken as positive.
(v) The distances measured downward and perpendicular to the principal axis are taken as negative.

Question 9:
An object 4 cm high is placed at a distance of 10 cm from a convex lens of focal length 20 cm. Find the position, nature and size of the image.
Solution : Question 10:
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.
Solution : Question 11:
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.
Solution : Question 12:
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.
Solution : Question 13:
An object is placed at a distance of 100 cm from a converging lens of focal length 40 cm.
(i) What is the nature of image ?
(ii) What is the position of image ?
A convex lens produces an inverted image magnified three times of an object placed at a distance of 15 cm from it. Calculate focal length of the lens.
Solution : Question 14:
A convex lens produces an inverted image magnified three times of an object placed at a distance of 15 cm from it. Calculate focal length of the lens.
Solution : Lakhmir Singh Physics Class 10 Solutions Page No:247

Question 15:
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 ?
Solution : Question 16:
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.
Solution : Question 17:
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 ?
Solution : Question 18:
An object 2 cm tall is placed on the axis of a convex lens of focal length 5 cm at a distance of 10 m 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 ?
Solution : Question 19:
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.
Solution : Question 20:
An erect image 2.0 cm high is formed 12 cm from a lens, the object being 0.5 cm high. Find the focal length of the lens.
Solution : Question 21:
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. Calculate the position, nature and size of the image.
Solution : Question 22:
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.
Solution : Question 23:
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 (upright) image of linear magnification 4.
Solution : Question 24:
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 ?
Solution : Question 25:
An object placed 4 cm in front of a converging lens produces a real image 12 cm from the lens.
(a) What is the magnification of the image ?
(b) What is the focal length of the lens ?
(c) Draw a ray diagram to show the formation of image. Mark clearly F and 2F in the diagram.
Solution : Question 26:
(a) An object 2 cm tall stands on the principal axis of a converging lens of focal length 8 cm. Find the position, nature and size of the image formed if the object is :
(i) 12 cm from the lens
(ii) 6 cm from the lens
(b) State one practical application each of the use of such a lens with the object in position (i) and (ii).
Solution : Question 27:
(a) An object 3 cm high is placed 24 cm away from a convex lens of focal length 8 cm. Find by calculations, the position, height and nature of the image.
(b) If the object is moved to a point only 3 cm away from the lens, what is the new position, height and nature of the image ?
(c) Which of the above two cases illustrates the working of a magnifying glass ?
Solution : Question 28:
(a) Find the nature, position and magnification of the images formed by a convex lens of focal length 0.20 m if the object is placed at a distance of :
(i) 0.50 m (ii) 0.25 m (iii) 0.15 m
(b) Which of the above cases represents the use of convex lens in a film projector, in a camera, and as a magnifying glass ?
Solution : Lakhmir Singh Physics Class 10 Solutions Page No:248

Question 41:
A student did an experiment with a convex lens. He put an object at different distances 25 cm, 30 cm, 40 cm, 60 cm and 120 cm from the lens. In each case he measured the distance of the image from the lens. His results were 100 cm, 24 cm, 60 cm, 30 cm and 40 cm, respectively. Unfortunately his results are written in wrong order.
(a) Rewrite the image distances in the correct order.
(b) What would be the image distance if the object distance was 90 cm ?
(c) Which of the object distances gives the biggest image ?
(d) What is the focal length of this lens ?
Solution : Question 42:
A magnifying lens has a focal length of 100 mm. An object whose size is 16 mm is placed at some distance from the lens so that an image is formed at a distance of 25 cm in front of the lens.
(a) What is the distance between the object and the lens ?
(b) Where should the object be placed if the image is to form at infinity ?
Solution : Question 43:
A lens forms a real image 3 cm high of an object 1 cm high. If the separation of object and image is 15 cm, find the focal length of the lens.
Solution : Lakhmir Singh Physics Class 10 Solutions Page No:249

Question 44:
An object 50 cm tall is placed on the principal axis of a convex lens. Its 20 cm tall image is formed on the screen placed at a distance of 10 cm from the lens. Calculate the focal length of the lens.
Solution : 