Lenses: Ray Diagrams and Magnification
A lens is a piece of transparent material, usually glass or plastic, with at least one curved surface that refracts light to form an image. A converging (convex) lens is thicker in the middle and bends parallel rays of light inward to meet at a principal focus; a diverging (concave) lens is thinner in the middle and spreads parallel rays outward, so they appear to come from a principal focus on the same side as the incoming light. The focal length is the distance from the centre of the lens to the principal focus. It covers constructing ray diagrams to locate images formed by converging and diverging lenses, describing images as real or virtual, upright or inverted, and magnified or diminished, and calculating magnification. It goes beyond the core GCSE course, which typically only asks students to name converging and diverging lenses, by requiring accurate scale ray diagrams and a required practical to find focal length using the lens equation.
Before you start
No specific prerequisites - this is a good place to start.
Method
- Decide whether the lens is converging (convex, bulges outward) or diverging (concave, curves inward), since the two rules for refracted rays are opposite.
- Draw the principal axis as a horizontal line through the centre of the lens, and mark the principal focus F and 2F at twice the focal length on both sides.
- Represent the object as a vertical arrow standing on the axis at the correct distance from the lens.
- From the top of the object draw two construction rays: one travelling parallel to the axis, which refracts through F on the far side for a converging lens (or appears to come from F on the near side for a diverging lens); and one passing straight through the centre of the lens undeviated.
- Mark where the two refracted rays actually cross (a real image) or where they appear to diverge from when traced backwards (a virtual image); drop a line to the axis to find the image's position and height.
- Describe the image using three pairs of terms: real or virtual, upright or inverted, and magnified, the same size, or diminished compared with the object.
- Calculate magnification using magnification = image height / object height; a magnification greater than 1 means the image is enlarged, and it has no unit because it is a ratio of two lengths.
Worked example
A converging lens has a focal length of 10 cm. An object of height 2.0 cm is placed 15 cm from the lens, producing a real image of height 6.0 cm. Calculate (a) the magnification of the image, and (b) the distance of the image from the lens, given that magnification = image distance / object distance.
- Write down the magnification equation using heights: magnification = image height / object height.
- Substitute the given heights: magnification = 6.0 / 2.0 = 3.0. Magnification has no unit, since it is the ratio of two lengths measured in the same unit.
- Write down the magnification equation using distances: magnification = image distance / object distance, so image distance = magnification x object distance.
- Substitute the object distance and the magnification found above: image distance = 3.0 x 15.
- Calculate: 3.0 x 15 = 45.
- State the final answer with its unit: the image forms 45 cm from the lens.
Practice questions
Try each question, then tap to reveal the answer.
Q1State the difference in shape between a converging lens and a diverging lens.Show answer
Answer: A converging lens is convex, thicker in the middle than at the edges; a diverging lens is concave, thinner in the middle than at the edges.
Q2A ray of light travels parallel to the principal axis and hits a converging lens. Describe the path it takes after refraction.Show answer
Answer: It refracts through the lens and passes through the principal focus on the far side of the lens.
Q3An object of height 5.0 cm produces a real image of height 15.0 cm. Calculate the magnification.Show answer
Answer: 3.0 (15.0 / 5.0), no unit.
Q4State whether the image formed by a diverging lens is always real or always virtual.Show answer
Answer: Always virtual, because the refracted rays spread apart and only appear to meet when traced backwards.
Q5A lens produces an image with a magnification of 0.50. State what this tells you about the size of the image compared with the object.Show answer
Answer: The image is diminished (smaller than the object), since the magnification is less than 1.
Q6In the required practical to find the focal length of a converging lens, name the three pieces of apparatus positioned along a metre rule.Show answer
Answer: An illuminated object, the converging lens, and a screen.
Q7An object of height 4.0 cm is placed close to a converging lens and produces a virtual, upright image of height 12.0 cm. Calculate the magnification.Show answer
Answer: 3.0 (12.0 / 4.0), no unit; magnification is calculated the same way for a virtual image.
Exam-style questions
Written in the style of a IGCSE Science exam paper, with a full mark scheme.
A student sets up a converging lens with an illuminated object and a screen to investigate how image distance v changes with object distance u. (a) Describe how the student should use the apparatus to obtain one pair of values of u and v. (2 marks) (b) The lens equation is 1/f = 1/u + 1/v. Given that the object distance is 30 cm and the image distance is 15 cm, calculate the focal length of the lens. (2 marks)
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A student carries out the required practical to determine the focal length of a converging lens using the lens equation 1/f = 1/u + 1/v. Describe how the student should collect a set of data and process it graphically to find the focal length, including what should be plotted and how the focal length is obtained from the graph.
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Free printable worksheet
Want more practice on paper? Download the lenses: ray diagrams and magnification worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 21 of IGCSE Science Workbook, the whole course as one free printable PDF.
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