3.2 Images formed by a convex lens Lens on a watch Image formation Construction rules Graphical construction of image formation Check-point 2 Position and nature of images Magnification Check-point 3 The lens formula Check-point 4 1 2 3 4 5 6 Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Lens on a watch Have you seen this kind of watch before? There is a lens over the date-display so that the date can be seen more easily. What kind of lens is this? Convex lens Book 3A Section 3.2 Images formed by a convex lens

3.2 Images formed by a convex lens Simulation 3.1 How images are formed by a convex lens Seeing an image formed by a convex lens Expt 3a Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Experiment 3a Seeing an image formed by a convex lens Place a convex lens 50 cm in front of a letter ‘F’ illuminated by a ray box. Move a translucent screen on the other side of the lens to capture a sharp image. Remove the screen and see if the image can still be observed. Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Experiment 3a Seeing an image formed by a convex lens Put the lens 5 cm away from the letter ‘F’ and see if the image can still be observed. 3.1 Expt 3a - Seeing images formed by a convex lens Video Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens 1 Image formation Convex lens can form real and virtual images. a Real images A small object is viewed through a convex lens. Object Y P Light rays from the object converge to point Y. If we look at the lens inside the region bound by the dotted lines (e.g. at P), a cone of rays will enter our eyes. Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens a Real images Object Y P   Q Since the rays cross at Y, our brain perceives the object at this position.  image at Y  real image (as light rays really diverge from it) We cannot see image at Q, as no light from the object enters our eyes. Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens a Real images We can place a translucent screen at Y to capture the image for viewing from different directions. Only real images can be captured by a screen. If the screen is moved forwards or backwards, a point on the object becomes a small patch of light on the screen image blurred Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens 1 Image formation b Virtual images An object is viewed through a convex lens placed very close to it. Light rays from the object still diverge after passing through the lens. Object P Our brain perceives them by extending them backwards. Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens 1 Image formation b Virtual images Extended rays meet at point Y Y Object P  Our brain perceives image there Virtual image (as no light rays actually pass through Y ) Virtual images cannot be captured on a screen. Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens 2 Construction rules Let us first investigate how light rays are refracted when they pass through a convex lens. Simulation 3.2 Refraction by a convex lens Construction rules for a convex lens Expt 3b Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Experiment 3b Construction rules for a convex lens Direct a light ray at a convex lens along the directions as shown. 2. Observe how the ray passes through the lens. 3.2 Expt 3b - Construction rules for a convex lens Video Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens 2 Construction rules From Expt 3b, we can summarize the construction rules for a convex lens: Rule 1 For a ray parallel to the principal axis, it is bent so that it passes through the principal focus F on the other side of the lens. Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens 2 Construction rules Construction rules for a convex lens: Rule 2 A ray passing through the principal focus F ’ emerges parallel to the principal axis. Rule 3 A ray passing through the optical centre travels straight on. Book 3A Section 3.2 Images formed by a convex lens

3 Graphical construction of image formation Ray diagrams are useful for locating images formed by lenses and figuring out their nature. We can use this symbol to represent convex lenses and apply the three construction rules. Book 3A Section 3.2 Images formed by a convex lens

3 Graphical construction of image formation Steps for drawing a ray diagram for a convex lens: Step 1 Draw the principal axis and convex lens. Step 2 Mark F ’ and 2F ’ on the principal axis on one side and F and 2F on the other side. (2F ’ = 2F = 2  focal length) Book 3A Section 3.2 Images formed by a convex lens

3 Graphical construction of image formation Step 3 Draw the object as an arrow upright on the principal axis at the given position. Book 3A Section 3.2 Images formed by a convex lens

3 Graphical construction of image formation Step 4 Draw rays (with arrows to indicate directions) from the tip using any two construction rules. If the refracted rays cross, the intersecting point is the location of the real image of the tip. Otherwise, use dotted lines for extending rays backwards to locate the virtual image. Book 3A Section 3.2 Images formed by a convex lens

3 Graphical construction of image formation Step 5 Draw the real image as a vertical arrow. Similarly, draw a dotted arrow as the virtual image. Simulation 3.3 Construction rules for a convex lens Example 1 Image formed by a convex lens Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Example 1 Image formed by a convex lens An object is placed between F ’ and 2F ’ from a convex lens. Four rays, p, q, r and s, from the object are incident on the lens. (a) Complete the rays and locate the image. (b) Is it a virtual or a real image? Real. Book 3A Section 3.2 Images formed by a convex lens

3 Graphical construction of image formation Parallel rays not parallel to the principal axis always converge to a point on the plane. This plane passes through the focus and ⊥ principal axis  focal plane If a screen is placed on the focal plane, it can capture the image of distant objects. Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Check-point 2 – Q1 Draw the rays of light after being refracted by the convex lens. Also mark the optical centre, principal axis and focal length of the lens. principal axis C f f Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Check-point 2 – Q2 Which emergent light ray is correct? Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Check-point 2 – Q3 (a) Complete the ray diagram. Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Check-point 2 – Q3 (b) Complete the ray diagram. Book 3A Section 3.2 Images formed by a convex lens

4 Position and nature of images Studying images formed by a convex lens Expt 3c Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Experiment 3c Studying images formed by a convex lens Set up the apparatus. Start with a large object distance (i.e. u > 2f ). Move the screen until a sharp image of is formed. Repeat step 2 with smaller object distances. Observe how the image changes. 3.3 Expt 3c - Studying images formed by a convex lens Video Book 3A Section 3.2 Images formed by a convex lens

4 Position and nature of images We describe the nature of an image by pointing out whether it is: (a) inverted or erect (b) magnified or diminished (c) real or virtual Expt 3c shows that: the position and nature of the image changes with the object distance.  use the construction rules to find them Book 3A Section 3.2 Images formed by a convex lens

4 Position and nature of images Distant object (object position: at infinity) Image position: on focal plane Image nature: Real, inverted, diminished Book 3A Section 3.2 Images formed by a convex lens

4 Position and nature of images Object position: beyond 2F ’ Image position: between F and 2F Image nature: Real, inverted, diminished Book 3A Section 3.2 Images formed by a convex lens

4 Position and nature of images Object position: 2F ’ Image position: 2F Image nature: Real, inverted, same size Book 3A Section 3.2 Images formed by a convex lens

4 Position and nature of images Object position: between F ’ and 2F ’ Image position: beyond 2F Image nature: Real, inverted, magnified Book 3A Section 3.2 Images formed by a convex lens

4 Position and nature of images Object position: F ’ Refracted rays are parallel, image formed at infinity (i.e. no image formed) Book 3A Section 3.2 Images formed by a convex lens

4 Position and nature of images Object position: within F ’ Image position: same side of the object Image nature: Virtual, erect, magnified For a convex lens, the nature of the image depends on the distance of the object from the lens. Simulation 3.4 Images formed by a convex lens Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens 5 Magnification Definition of magnification m: height of image (image size) height of object (object size) = hi ho = m image distance object distance = v u = or m Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens 5 Magnification When magnification > 1,  the image is magnified When magnification < 1,  the image is diminished When Magnification = 1,  the image is of the same size Example 2 Finding the image on graph paper Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Example 2 Finding the image on graph paper Object: 5 cm high, 15 cm from a convex lens Focal length of convex lens = 10 cm Find the position and magnification of the image. Draw a ray diagram. Image distance = 6 × 5 = 30 cm v u = 30 15 = m = 2 Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens 5 Magnification Example 3 Viewing through a magnifying glass Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Example 3 Viewing through a magnifying glass Amy is using a convex lens to view the newspaper. The figure shows what she sees. (a) Estimate the magnification of the image. Magnification = image size object size 3 1 = = 3 (b) State the nature of the image. Virtual, erect and magnified. Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Example 3 Viewing through a magnifying glass (c) The lens is held at 5 cm from the page. Drawing a ray diagram find the focal length of the lens. From the ray diagram, focal length = 7.5 cm. Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens 5 Magnification Example 4 Refracting telescopes Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Example 4 Refracting telescopes Convex lenses are used in many imaging instruments. Usually two lenses are used instead of one since the overall magnification is much larger. E.g. two convex lenses of different focal lengths are used in a refracting telescope. Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Example 4 Refracting telescopes The telescope is adjusted so that the focal planes of the two lenses coincide. The image formed by the objective acts as the object of the eyepiece. Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Example 4 Refracting telescopes (a) When the telescope is used to view a star, where is the image formed by the objective? On the focal plane of the objective lens. (b) Hence, where is the image formed by the eyepiece? At infinity. Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Example 4 Refracting telescopes fo fe (c) Magnification of the final image = , where fo and fe = focal lengths of objective and eyepiece respectively. How to increase the magnification of the telescope? Use an objective of longer focal length and an eyepiece of shorter focal length. Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Check-point 3 – Q1 Complete the following table for a convex lens: Object position Image position Nature of image < F ’ Same side as the object Virtual, erect, magnified F ’ >F ’ and <2F ’ 2F ’ > 2F ’ At infinity At infinity No image is formed > 2F Real, inverted, magnified 2F Real, inverted, same size >F ’ and <2F ’ Real, inverted, diminished on focal plane Real, inverted, diminished Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Check-point 3 – Q2 The virtual images formed by a convex lens must be _________ than the object. larger Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Check-point 3 – Q3 A boy looks at a poster through a magnifying glass and sees a magnified erect image. What happens to the image if he moves the lens closer to his eyes? A It gets larger till it gets totally blurred B It gets larger, keeping erect all the way. C It gets smaller and becomes totally blurred. D It gets smaller, keeping erect all the way. Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens 6 The lens formula Expt 3d The lens formula Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Experiment 3d The lens formula Set up the apparatus using a convex lens with a known f. Set u > f . Move the screen until a sharp image is formed. Record u and v. 3. Repeat step 2 with different values of u. Record the corresponding values of v. Video 3.4 Expt 3d - The lens formula Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens 6 The lens formula From Expt 3d, we have the Lens formula: 1 u v f + = can be applied to both real and virtual images the ‘real-is-positive’ convention is used: Focal length f Object distance u Image distance v Real Virtual Sign + – Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens 6 The lens formula Let’s use lens formula to solve Example 2. Substitute u = 15 and f = 10: 1 15 v 10 + = 1 15 v 10 – =   v = 30 m = v u 30 15 = = 2 The same result is obtained! Example 5 Focal length of a magnifying glass Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Example 5 Focal length of a magnifying glass Detective Holmes is investigating a crime scene. He puts a convex lens 2 cm away from a wall. image is erect magnification = 3 Focal length of the lens = ? Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Example 5 Focal length of a magnifying glass u = 2 cm m = 3 image is erect m = v u  v = mu = 3 × 2 = 6 The image is virtual (∵erect and magnified). ∴ Image distance should be taken as –ve. 1 u v f + = 1 2 (–6) + =  f = 3 Focal length of the lens is 3 cm. Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Check-point 4 – Q1 An object is placed 3 cm away from a convex lens. If f = 6 cm, which of the following gives the best description for the image? A virtual image, 6 cm away from the lens B real image, 6 cm away from the lens C virtual image, 3 cm away from the lens D real image, 3 cm away from the lens Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens Check-point 4 – Q2 Determine the focal length of the convex lens. 1 u v f + = 1 4 12 + =  f = 3 Focal length of the lens is 3 cm. Book 3A Section 3.2 Images formed by a convex lens

Book 3A Section 3.2 Images formed by a convex lens The End Book 3A Section 3.2 Images formed by a convex lens