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Reflection, Refraction and Lenses: Question 2

Syllabus 3.2.1

Structured Core 7 marks

A dance studio has a large vertical plane mirror fixed to one wall so that dancers can check their posture during rehearsals.

(a) State three characteristics of the image of a dancer formed in the plane mirror. [3]

(b) One dancer stands close to the mirror, while a second dancer stands further away, on the same side of the mirror. State how the distance of each dancer's image behind the mirror compares with the distance of that dancer in front of the mirror. [2]

(c) One of the dancers wears a T-shirt with the word "DANCE" printed on the front, facing the mirror. State how this word would appear in the dancer's image, and name the property of the image that explains this. [2]

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Worked solution

Part (a): Characteristics of the image

A plane mirror always forms an image with the same set of properties, no matter how far away the object stands:

  • Virtual, the rays only appear to come from behind the mirror; the image cannot be formed on a screen.
  • Same size as the object (magnification of 11).
  • Laterally inverted. Left and right are swapped.
  • Upright, not upside down.
  • The image is the same distance behind the mirror as the object is in front.

Any three of these count as full credit.

Part (b): Comparing the two dancers’ images

For a plane mirror, each image forms as far behind the mirror as that object is in front of it. This rule applies separately to each dancer.

  • The dancer standing close to the mirror has an image that is also close behind the mirror.
  • The dancer standing further away has an image that is correspondingly further behind the mirror.

So the two dancers do not share the same image distance: each dancer’s own object distance and image distance are equal to each other, but the two dancers’ distances differ from one another because they are standing at different distances from the mirror.

Part (c): Lateral inversion of the printed word

A plane-mirror image is laterally inverted, reversed from left to right (though not upside down). Printed text is especially sensitive to this, because the order and orientation of the letters both flip horizontally.

So the word “DANCE” would appear reversed left-to-right in the mirror. It would not read normally as “DANCE” when viewed directly in the image. This is a direct consequence of the mirror’s lateral inversion, and it is the reason ambulance vehicles, for example, often have their name printed in mirror-writing on the front so it reads correctly to a driver looking in their rear-view mirror.

Final answers

  • (a) Any three of: virtual; same size; laterally inverted; upright; same distance behind the mirror as the object is in front
  • (b) Each dancer’s image distance behind the mirror equals that dancer’s own distance in front of the mirror. The closer dancer has the closer image, the further dancer has the further image
  • (c) The word appears laterally inverted (reversed left-to-right), because the plane-mirror image is laterally inverted