3.3 Images formed by a concave lens The peephole Image formation Construction rules Graphical construction of image formation Check-point 5 Position and nature of images Magnification Check-point 6 The lens formula Check-point 7 1 2 3 4 5 6 Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens The peephole Have you ever look through the peephole? How does the image look like? erect, diminished The peephole consists of a concave lens. Why a concave lens is used? to identify visitors and the environment Book 3A Section 3.3 Images formed by a concave lens

3.3 Images formed by a concave lens Can concave lens also form both real and virtual images? Simulation 3.5 How images are formed by a concave lens Seeing an image formed by a concave lens Expt 3e Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens Experiment 3e Seeing an image formed by a concave lens Look through the concave lens to see the image of a letter ‘F’ from a ray-box. Try to capture a image by a translucent screen. Repeat steps 1 and 2 with different object distances. 3.5 Expt 3e - Seeing images formed by a concave lens Video Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens 1 Image formation Expt 3e shows that image formed by concave lens can never be captured on a screen.  only virtual images formed Light rays from the object always diverge after passing through the concave lens. Our brain perceives an image at Y. No light rays actually pass through Y. Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens 2 Construction rules Simulation 3.6 Refraction by a concave lens Expt 3f Construction rules for a concave lens Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens Experiment 3f Construction rules for a concave lens Direct a light ray at a concave lens along the directions as shown. 2. Observe how the ray passes through the lens. 3.6 Expt 3f - Construction rules for a concave lens Video Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens 2 Construction rules Construction rules for a concave lens: Rule 1 A ray parallel to the principal axis is bent so that it appears to come from the principal focus F’. Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens 2 Construction rules Construction rules for a concave lens: Rule 2 A ray directed towards the principal focus F is bent parallel to the principal axis. Rule 3 A ray passing through the optical centre travels straight on. Book 3A Section 3.3 Images formed by a concave lens

3 Graphical construction of image formation The symbol used to represent concave lens in ray diagrams: Steps for drawing a ray diagram for a concave lens: Step 1 Draw the symbol of concave lens and the principal axis. Book 3A Section 3.3 Images formed by a concave lens

3 Graphical construction of image formation Step 2 Mark F ’, 2F ’, F and 2F on the principal axis. Step 3 Draw the object on the principal axis at the given position. Book 3A Section 3.3 Images formed by a concave lens

3 Graphical construction of image formation Step 4 Draw rays from the tip of the object using any two of the construction rules. Use dotted lines for extending rays backwards to locate the virtual image. Book 3A Section 3.3 Images formed by a concave lens

3 Graphical construction of image formation Step 5 Draw a dotted arrow as the virtual image with its tail on the principal axis. Simulation 3.7 Construction rules for a concave lens Example 6 Image formed by a concave lens Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens Example 6 Image formed by a concave lens Four rays, p, q, r and s, from the object are incident on a concave lens. (a) Complete the rays and locate the image. (b) Is it a virtual or a real image? Virtual. Book 3A Section 3.3 Images formed by a concave lens

3 Graphical construction of image formation Note: Parallel rays that not parallel to the principal axis always appear to diverge from a point on the focal plane. Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens Check-point 5 – Q1 Draw the rays of light after being refracted by the concave lens. Also mark the optical centre, principal axis and focal length of the lens. principal axis C f f Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens Check-point 5 – Q2 Which of the following incident rays is mentioned in the construction rules? A B Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens Check-point 5 – Q3 How to find the focus of the lens? Step 1: Draw ray A parallel to the principal axis from the tip of the object O. Step 2: After passing through the lens, ray A appears to come from the ________ and the extended part __________the tip of the image. focus touches Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens Check-point 5 – Q3 How to find the focus of the lens? Step 3: The point where the extended part crosses the ______________ is the focus.  F principal axis Book 3A Section 3.3 Images formed by a concave lens

4 Position and nature of images Images formed by a concave lens: Distant object (position: at infinity) Image position: on focal plane, same side Image nature: Virtual, erect, diminished Book 3A Section 3.3 Images formed by a concave lens

4 Position and nature of images Object position: between the lens and  Image position: <F ’, same side Image nature: Virtual, erect, diminished Book 3A Section 3.3 Images formed by a concave lens

4 Position and nature of images From the results above, we can conclude that: For concave lenses, the image is always virtual, erect and diminished. Simulation 3.8 Images formed by a concave lens Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens 5 Magnification magnification m hi ho = v u Example 7 Finding the image on graph paper Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens Example 7 Finding the image on graph paper Object : 5 cm high, 15 cm from a concave lens Focal length = 10 cm Find the position and magnification of the image. Draw a ray diagram on a graph paper. Image distance = 1.2 × 5 = 6 cm v u = 6 15 = m = 0.4 Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens 5 Magnification Video 3.7 Coin box Images formed by a camera Example 8 Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens Example 8 Images formed by a camera In a single-lens reflex camera, the distance between the lens and the image sensor can be adjusted so that objects at different places can be put into focus. Object: 1.2 m in front of the camera (a) Explain briefly what kind of lens A is. It is a convex lens since real images are formed on the image sensor. Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens Example 8 Images formed by a camera (b) Focal length of the lens = 200 mm (i) Find the distance between the lens and the image sensor by drawing a ray diagram. Distance = 1.2 × 200 = 240 mm (ii) Find the magnification of the image. Magnification = v u 240 1200 = = 0.2 Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens Example 8 Images formed by a camera (c) Now, lens A is replaced with lens B (same type but with a different f ). The magnification increases. (i) How should the distance between the lens and the sensor change so that a clear image can be formed on the sensor? ∵Image distance  when magnification . ∴The distance between the lens and the sensor should be increased. Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens Example 8 Images formed by a camera (c) (ii) In order to get a wider view, should lens A or B be used? The smaller the m, the wider the view.  lens A should be used. (d) Compare the images formed by a convex lens and a concave lens if the object distance is 2f. Convex lens: real, inverted, same size Concave lens: virtual, erect, diminished Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens Check-point 6 – Q1 The images formed by a concave lens are always ____________ , __________ and ________________ . virtual erect diminished Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens Check-point 6 – Q2 Complete the table for a concave lens: Object position Image position Nature of image Between lens and infinity At infinity Within F ’, same side as the object Virtual, erect, diminished On focal plane, same side as the object Virtual, erect, diminished Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens Check-point 6 – Q3 What is the magnification of the image formed by the concave lens? A 0.2 B 0.5 C 2 D 5 Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens 6 The lens formula 1 u v f + = The lens formula also applies to concave lenses. In the ‘real-is-positive’ convention: the focal length of a concave lens is –ve. the image distance is always –ve as only virtual images are formed Simulation 3.9 Lens formula Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens 6 The lens formula Apply the lens formula to solve Example 7. Substitute u = 15 and f = –10: 1 15 v –10 + = 1 15 v –10 – =  v = –6  m = v u 6 15 = = 0.4 The same results are obtained! Finding the focal length using the lens formula Example 9 Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens Example 9 Finding the focal length using the lens formula Object: 9 cm in front of the lens Image: virtual, 3 cm from the lens. (a) Find the focal length of the lens. Applying the lens formula: 1 u v f + = 1 9 –3 + =  f = –4.5 (b) What kind of lens is this? The value of f is –ve  concave lens Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens 6 The lens formula Example 10 View through a lens Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens Example 10 View through a lens Sam is using a lens to view a piece of ruled-paper. (a) State the nature of the image. What kind of lens is this? The image is diminished and erect. This is a concave lens. (b) Estimate the magnification of the image. Magnification = image size object size 1 2 = = 0.5 Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens Example 10 View through a lens (c) Find the distance between the lens and the ruled-paper if the f = 6 cm. m = v u  v = mu = 0.5u Substitute v = –0.5u and f = –6: 1 u v f + = 1 u –0.5u –6 + =  1 – 2 u 1 –6 =   u = 6 Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens Check-point 7 – Q1 Put ‘+’ or ‘–’ signs in the appropriate boxes to represent their signs. + Image distance of a real image Image distance of a virtual image Focal length of a convex lens Focal length of a concave lens – + – Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens Check-point 7 – Q2 An object 30 cm from a concave lens produces a virtual image 15 cm from the lens. What is the focal length of the concave lens? A 30 cm B 10 cm C –10 cm D –15 cm Book 3A Section 3.3 Images formed by a concave lens

Book 3A Section 3.3 Images formed by a concave lens The End Book 3A Section 3.3 Images formed by a concave lens