3. Convex lens ray diagram for when object is at a distance of 2F (2 x focal length) from the lens

Ray diagram 3a (below): Ray diagram showing the formation of an image from an object O at a distance of 2F from the convex lens (twice the focal length) beyond the convex lens.

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• 3a converging convex lens

• To construct the ray diagram 3a, draw a vertical line tipped with an arrow for the object O, at the appropriate distance from the lens, in this case a distance exactly 2F from the lens.

  • Imagine the object is standing on the principal axis of the lens.

  • Apart from the axis line, this is essentially a 2 ray diagram for an object 'standing' on the axis line.

• (i) Draw a ray from the arrow tip of the object parallel to the principal axis into the lens.

  • Since this ray is parallel to the axis, beyond the lens, the ray must continue down through the principal focus F (in this case beyond a 2F distance 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, diagonally down through the centre of the lens, and continue the line until it is beyond intersecting with the first ray (i) you drew.

  • Again, check this line in ray diagram 3a above, which must pass through the centre of the lens without deviation.

  • A ray passing through the centre of a lens is considered NOT to be deviated - NOT refracted.

  • Please remember this applies to ANY lens, and, for convex lenses only, a ray parallel to the principal axis, after refraction, passes through the principal focus point F, when studying the rest of the diagrams on this page.

• 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 the diagram you can see that the image I is real (formed directly by converging rays, inverted (upside down) and the same size as the object O and at a distance of exactly 2F beyond the lens on the opposite side from the object.

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• 3b converging convex lens

• Above is quick sketch 3b of how to do the ray diagram 3a on graph paper.

  • If done very carefully to scale, you can then calculate the height of the image I and the distance from the lens to the image I.

• Below is a more elaborate graph paper ray diagram 3c for a convex lens where the object is placed at a distance of 2F from the lens and O is placed 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.

3c

• (i) Draw a line from the top of the object to the lens and, after the lens, down through the focal point F.

• (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.