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Lens formula =

Magnification: The ratio of the size (height) of the image to the size (height) of the object is called magnification (M). Mathematically,

Magnification, M = size of the image (I)/size of the object (O)

= Height of the image (h1)/ Height of the object (h0)

Magnification, M = Distance of the image from the lens/Distance of the object from the lens

= v/u

The sign of the magnification of a lens gives information about the nature of the image produced by it. So, if

Sign of the magnification: -ve Image: inverted and real

Sign of the magnification: +ve Image: Erect and virtual

The magnitude of the magnification of a lens gives information about the size of the image relative to that of the object. So, when

Magnitude of the magnification = 1 size of the image = size of the object

Magnitude of the magnification > 1 size of the image > size of the object

Magnitude of the magnification < 1 size of the image < size of the object

Power of a lens: Power of a lens is defined as the reciprocal of its focal length in meters. It is measured in dioptres denoted by the letter D. The dioptre unit is equal to m-1 i.e. 1 D = 1 m-1

Power of a lens = (1/Focal length of the lens in m ) D

Exercise

1. An object of 4.5 cm height is placed 20cm from a convex lens of focal length 12 cm. Find the nature, position and height of the image. 2. Find the position and the nature of the image formed by a concave lens of focal length 15 cm, of an object placed at a distance of 5 cm in front of it. What is its magnification?

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3. 1 cm high object is placed at a distance of 2f from a convex lens. What is the height of the image formed? 4. An object of height 5 cm is kept 25 cm away from a converging lens of focal length 10 cm. Draw a ray diagram and find the position, size and nature of the image formed. 5. Find the position, size and nature of the image of an object 5 cm high which is placed 10 cm in front of a convex lens if focal length 6 cm 6. The lens of a camera has a focal length of 10 cm. what must be the distance between the lens and the film in order to photograph object at (a)infinity (b)20 cm from the lens. 7. An object is placed at a distance of 0.5 m from a concave lens of focal length of 0.2 m. find the nature and position of the image 8. An object place 50 cm from a lens produces a virtual image at a distance of 10 cm in front of the lens. What is the focal length of lens? Is it converging or diverging lens? 9. A convex lens has focal length of 30 cm. Calculate at what distance should the object be placed from the lens so that it forms an image at 60 cm on the other side of the lens? Find the magnification produced by the lens? 10. An object is placed at a distance of 50 cm from a concave lens of focal length 20 cm. Find the nature and position of the image. 11. A diverging lens of focal length 15 cm forms an image 10 cm from the lens. Draw a scale diagram and prove that the object is placed 30 cm away from the lens. Use a scale of 1:5 12. An object placed 50 cm from a lens produced a virtual image at a distance of 10 cm in front of the lens. Draw a diagram to show the formation of image and calculate the focal length of the lens. 13. Find the position and nature of the image formed when an object is placed at a distance of 5 cm from a concave lens of focal length 15 cm. What is its magnification? 14. An object 5 cm high is placed at a distance of 30 cm from a convex lens of focal length 15 cm. find the position and nature of the image. 15. A real image, 1/5th of the size of the object is formed at a distance of 18 cm from a lens. What is the nature of the lens and calculate its focal length. 16. An object located 32 cm in front of a lens forms an image on a screen 8 cm behind the lens.(i)find the focal length of the lens (ii)determine the magnification (iii)is the lens converging or diverging. 17. What is the power of the lens having a focal length (a) 25 cm (b) -25 cm 18. The power of a lens is 2.5 dioptre. What is the focal length and the type of the lens. 19. A person having a myopic eye uses a concave lens of focal length 50 cm, what is the power of the lens. 20. A person can se clearly only up to 3.5 m what king of lens does he required to correct his vision? What should be the focal length and power of such a lens

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