Everything Science Grade 11

13.2 CHAPTER 13. GEOMETRICAL OPTICS

Object

Image

F 1

F 2

O

R 1

R 3

R 2

f f f f

Figure 13.8: An objectis placed at a distance equal to 2 f away from the converging lens. Three rays
are drawn to locate theimage, which is real, thesame size as the objectand inverted.

CASE 2:

Object placed at a distance equal to 2 f from the lens

We can locate the position of the image by drawing our three rays. R 1 travels from the object to the
lens parallel to the principal axis and is bent bythe lens and then travels through the focal point. R 2
passes through the focal point before it entersthe lens and therefore must leave the lens parallel to
the principal axis. R 3 travels through the centre of the lens and doesnot change direction. The point
where R 1 , R 2 and R 3 intersect is the image ofthe point where they allstarted.

The image of an object placed at a distance equal to 2 f from the lens is upsidedown or inverted. This
is because the rays which began at the top of theobject, above the principal axis, afterpassing through
the lens end up below the principal axis. The image is called a real image because it is on the opposite
side of the lens to the object and you can traceall the light rays directlyfrom the image back tothe
object.

The image is the same size as the object and islocated at a distance 2 f away from the lens.

CASE 3:

Object placed at a distance between 2 f and f from the lens

Object

Image

F 1

F 2

O

R 1

R 3

R 2

f f f f

Figure 13.9: An object is placed at a distance between 2 f and f away from the converging lens. Three
rays are drawn to locatethe image, which is real, larger than the object and inverted.

We can locate the position of the image by drawing our three rays. R 1 travels from the object to the
lens parallel to the principal axis and is bent bythe lens and then travels through the focal point. R 2
passes through the focal point before it entersthe lens and therefore must leave the lens parallel to
the principal axis. R 3 travels through the centre of the lens and doesnot change direction. The point
where R 1 , R 2 and R 3 intersect is the image ofthe point where they allstarted.