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Lenses and images questions
A lens is refraction put to work, glass shaped so that every ray leaving a point meets again at another point. Get the geometry of that meeting under control and cameras, spectacles, magnifying glasses and the eye itself all reduce to one exam question.
21 original questions · 63 marks · the lenses and images notes · Waves
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State what is meant by the principal focus and the focal length of a converging lens.
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The principal focus is the point where rays arriving parallel to the principal axis are brought together after passing through the lens (1). The focal length is the distance from the centre of the lens to the principal focus (1).Calculate the power of a converging lens of focal length 40 cm, giving the unit.
Mark scheme
f = 40 cm = 0.40 m (1)
P = 1/f = 1/0.40 = 2.5 D, dioptres (1)State the difference between a real image and a virtual image.
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A real image is formed where rays actually meet, so it can be caught on a screen (1). A virtual image is formed where rays only appear to come from when projected backwards; no rays pass through it and no screen can catch it (1).An object is placed in front of a diverging lens. State the nature of the image formed.
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Virtual: it forms where the spreading refracted rays appear to come from, on the same side of the lens as the object (1). It is upright and diminished (1).A converging lens is used to photograph a distant building. State where the image forms, and give its nature.
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The image forms in the focal plane: the image distance is (approximately) equal to the focal length, because 1/u is negligible for a distant object (1). It is real, inverted and diminished (1).A student writes the magnification of an image as m = 0.60 m. State the error the student has made.
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Magnification is a ratio of two lengths (v/u, or image height over object height), so it has no unit; the metre should not appear (1).An object is placed 0.45 m from a converging lens of focal length 0.15 m. Calculate the image distance and the magnification.
Mark scheme
1/v = 1/f − 1/u = 1/0.15 − 1/0.45 (1)
v = 0.225 m ≈ 0.23 m (1)
m = v/u = 0.50 (1)Describe the paths of the three standard construction rays used to locate the image formed by a thin converging lens.
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A ray parallel to the principal axis refracts to pass through the principal focus on the far side (1). A ray through the centre of the lens continues undeviated (1). A ray passing through the near principal focus leaves the lens parallel to the axis (1). Any two fix the image; the third confirms it.An object is placed 0.10 m from a converging lens of focal length 0.25 m. Calculate the image position, state the nature of the image, and give its magnification.
A student covers the top half of a lens with card and predicts the top half of the image will vanish. State and explain what actually happens.
A diverging lens has a power of −4.0 D. Calculate its focal length.
An object is placed 60 cm from a converging lens of power +2.5 D. Calculate the image distance and the magnification.
A converging lens of focal length 0.15 m forms a real image three times the height of the object. Calculate the object distance and the image distance.
An object 2.0 cm tall stands 0.80 m from a converging lens of focal length 0.25 m. Calculate the height of the image and state its orientation.
A lens forms a real image on a screen 0.60 m away when the object is 0.30 m from the lens. Calculate the focal length of the lens.
A +4.0 D converging lens is placed in contact with a −1.5 D diverging lens. Calculate the power and focal length of the combination.
A projector lens of focal length 5.0 cm throws a sharp image on a screen 3.0 m away. Calculate the object distance, and the magnification of the image on the screen.
Explain, in terms of the images they form, why a magnifying glass must hold the object inside the focal length, and what happens to the image as the object slides out towards the focal point.
A camera has a converging lens of focal length 50 mm which moves towards or away from the sensor to focus. Calculate how far, and in which direction, the lens must move from its position when focused on a very distant object so that an object 1.2 m away is in focus.
A student must project the image of a slide onto a screen fixed 2.4 m from the lens, with the image at least 20 times the height of the slide. Two converging lenses are available:
Lens L1: focal length 0.10 m.
Lens L2: focal length 0.25 m.
Deduce which lens the student should use, and state the distance from the slide to the lens.Describe an experiment to determine the focal length of a converging lens, using an illuminated object, the lens, a screen and a metre rule. Include the measurements taken, how the focal length is found from them, and one way to check or improve the result.
The same practice on paper: the printable workbook for this topic, questions and a worked answer book.
Practise lenses and images one question at a time
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