GCSE Physics How to construct convex lens ray diagram when object O is a distance between F and 2F from lens (between focal length and 2 x focal length of lens) image real inverted bigger than object IGCSE/GCSE Physics revision notes

GCSE level Physics exam revision notes on OPTICS

Optics: Lenses: Part 4. Constructing the convex lens ray diagram for when the object O is a distance between F and 2F from lens (between focal length and 2 x focal length of lens)

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INDEX of notes on optics: lens types, properties, correcting eye defects

4. Convex lens ray diagram for when object is a distance between F and 2F from lens (between focal length and 2 x focal length of lens)

Ray diagram 4 (below): The formation of a real image by a convex lens when the object O is a distance from the convex lens between F and 2F.
- 4a converging lens
- You construct this ray diagram 4a as exactly described for ray diagram 3.
  - Apart from the axis line, this is essentially a 2 ray diagram for an object 'standing' on the axis line of the lens.
- (i) Draw a ray from the arrow tip parallel to the principal axis into the lens.
  - Since this is parallel to the axis, beyond the lens, the ray must continue down through the principal focus (in this case beyond a distance of 2F to the right of the lens). Check this line in ray diagram 2 above.
- (ii) You then draw a line, again from the top of the object, down through the centre of the lens, and continue the line until it is beyond intersecting with the first ray you drew.
- The intersection point gives you the position of the bottom of the image and the inverted arrow gives you the size of image I. From this you can see that ....
- The image is real, inverted and larger than the object and on the opposite side from the object.
- The image is further than a distance beyond 2F from the lens on the image side of the lens.
- So here the convex lens is acting as a magnifying glass.
- 4b convex lens
- Above is quick sketch of how to do the ray diagram 4a on graph paper.
- If done very carefully to scale, from diagram 4b, you can then calculate the height of the inverted image I and the distance from the lens to the image I.
- From the graph, and measuring in 'squares' you can work out the ...
- magnification = size of image / size of object = 8 / 5 = 1.6
Below is a more elaborate graph paper ray diagram 4c for a convex lens where the object is placed at a distance between F and 2F from the lens, BUT, above the central axis of the lens - four rays are marked (i) to (iv), each intersecting pairs of lines ('rays') gives you the top and the bottom of the image.

(i) Draw a line from the top of the object to the lens and, after the lens, down through the focal point F to well beyond a distance of 2F.
(ii) Draw a diagonal line from the top of the object down through the centre of the lens and beyond the intersection with ray (i).
- The intersection of rays (i) and (ii) gives you the position of the bottom of the inverted image.
(iii) Draw a line from the bottom of the object parallel to the principal axis and, after the lens, diagonally down through F.
(iv) Draw a line from the bottom of the object diagonally down through the centre of the lens and beyond the intersection with ray (iii).
- The intersection of rays (iii) and (iv) gives you the position of the top of the inverted image.
From the graph, and measuring in 'squares' you can work out the ...
magnification = size of image / size of object = 9 / 5 = 1.8

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Keywords, phrases and learning objectives for properties and uses of lenses

Know how to construct the convex lens ray diagram when the object O is at a distance between F and 2F from the centre of the lens (between focal length and 2 x focal length of lens).

Know and explain why the image is real, inverted and larger than the object O.

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