Reflection, Refraction and Lenses: Question 5
Syllabus 3.2.3
A collector uses a converging lens as a magnifying glass to examine the fine engraving on an antique pocket watch. The lens has a principal focal length of . The collector holds the lens so that the watch face is from the lens, closer to the lens than the principal focal length, and looks through the lens from the other side.
(a) Explain why the watch face must be placed closer to the lens than the principal focal length for the lens to work as a magnifying glass. [2]
(b) Describe how you would construct a ray diagram to locate the image of a point on the watch face, using two rays whose paths through a converging lens are known, and state where the image is formed relative to the lens and the watch face. [3]
(c) State three characteristics of the image seen by the collector. [3]
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Worked solution
Part (a): Why the object must be inside the focal length
A converging lens only produces a magnified, upright, virtual image, the kind needed for a magnifying glass, when the object is placed closer to the lens than the principal focal length.
In that case, light rays leaving a point on the object are refracted by the lens but are still diverging as they leave it; they never actually meet on the far side, so no real image forms there. The collector’s eye, looking through the lens, follows these diverging rays back to the point from which they appear to have spread out. This apparent point lies on the same side of the lens as the watch face, further from the lens than the watch face itself, and gives an enlarged, upright image.
If the watch face were placed beyond the focal length instead, the lens would form a real, inverted image on the far side, which is not what is wanted when looking directly through the lens as a magnifying glass.
Part (b): Constructing the ray diagram
Two rays with known paths through a converging lens can be used to locate the image of a point on the watch face:
- A ray from the point, travelling parallel to the principal axis. On refraction, this ray is directed towards the principal focus on the far side of the lens (the same rule that applies for any object position).
- A ray from the same point, passing through the centre of the lens, which continues undeviated in a straight line.
Because the watch face is inside the focal length, these two rays are still diverging as they travel away on the far side of the lens, they never actually cross there. To locate the image, both rays must be extended backwards (dashed lines, back through the lens and onto the object’s side) until they meet.
The point where they meet, on the same side of the lens as the watch face but further from the lens than the watch face itself, locates the image of that point. The collector’s eye, positioned close to the lens on the far side, looks back through the lens towards the watch face to see this image.
Part (c): Characteristics of the image
Since the image is only located by extending rays backwards, and light does not actually pass through it, the image is:
- Virtual, it cannot be formed on a screen, because no real light rays meet there.
- Upright, the same way up as the watch face, not inverted.
- Magnified. Larger than the watch face itself, which is exactly why the lens is useful as a magnifying glass.
Final answers
- (a) With the object inside the focal length, the emerging rays still diverge and never form a real image; tracing them back gives a virtual, upright, magnified image, the effect a magnifying glass relies on
- (b) Use the ray parallel to the axis (refracts towards the far-side focus) and the ray through the lens centre (undeviated); extend both backwards until they meet, on the object’s side of the lens but further from it, to locate the image
- (c) The image is virtual, upright, and magnified