FOCUS POINT
SECTION 3 Waves
3.2.3 Thin lenses
▲ Figure 3.2.36a A converging lens forms a magnified image of a close object.
▲ Figure 3.2.36b A diverging lens always forms a diminished image.
Principal focus
When a beam of light parallel to the principal axis passes through a converging lens it is refracted so as to converge to a point on the axis called the principal focus (focal point), F. It is a real focus.
A diverging lens has a virtual principal focus behind the lens, from which the refracted beam seems to diverge.
Since light can fall on both faces of a lens it has two principal foci, one on each side, equidistant from C. The distance CF is the focal length f of the
lens (see Figure 3.2.35a); it is an important property of a lens. The more curved the lens faces are, the smaller is f and the more powerful is the lens.
Key definitions
Principal focus (focal point) point on the principal axis of a lens to which light rays parallel to the principal axis converge, or appear to diverge from
Focal length distance between the optical centre and the principal focus of a lens
Practical work
Focal length, f, of a converging lens Safety
l Never look at the Sun directly or through a lens.
We use the fact that rays from a point on a very distant object, i.e. at infinity, are nearly parallel (Figure 3.2.37a).
very distant
point parallel beam
distant point
almost parallel beam close point diverging beam
▲ Figure 3.2.37a
3.2.3 Thin lenses
Move the lens, arranged as in Figure 3.2.37b, until a sharp image of a window at the other side of the room is obtained on the screen.
The distance between the lens and the screen is then f, roughly.
light from window at other side of room
lens
ruler screen or wall
▲ Figure 3.2.37b
18 Why is the distance between the lens and the screen f, roughly?
19 Why could the focal length of a diverging lens not be found by the method suggested in the practical?
Images formed by a converging lens In the formation of images by lenses, two important points on the principal axis are F and 2F; 2F is at a distance of twice the focal length from C.
First find the focal length of the lens by the distant object method just described, then fix the lens upright with Plasticine at the centre of a metre ruler. Place small pieces of Plasticine at the points F and 2F on both sides of the lens, as in Figure 3.2.38.
Place a small light source, such as a torch bulb, as the object supported on the ruler beyond 2F and move a white card, on the other side of the lens from the light, until a sharp image is obtained on the card.
Note and record, in a table like the one opposite, the image position as ‘beyond 2F’, ‘between 2F and F’ or ‘between F and lens’. Also note whether
the image is enlarged or diminished compared with the actual bulb or the same size and if it is upright or inverted. Now repeat with the light at 2F, then between 2F and F.
Plasticine metre ruler
screen
torch converging lens
2F F F 2F
▲ Figure 3.2.38
Object position Image position
Enlarged, diminished or same size?
Upright or inverted?
beyond 2F at 2F
between 2F and F between F and lens
So far, all the images have been real since they can be obtained on a screen. When the light is between F and the lens, the image is virtual and is seen by looking through the lens at the light.
Do this. Record your findings in your table.
20 a Is the virtual image enlarged or diminished?
b Is it upright or inverted?
21 Using your results, draw ray diagrams to locate the image for each of your object positions. Do the values you obtain agree with your measured values
a beyond 2F b at 2F
c between 2F and F d between F and lens?
Ray diagrams
Information about the images formed by a lens can be obtained by drawing two of the following rays.
(i) A ray parallel to the principal axis which is refracted through the principal focus, F.
(ii) A ray through the optical centre, C, which is undeviated for a thin lens.
(iii) A ray through the principal focus, F, which is refracted parallel to the principal axis.
In diagrams a thin lens is represented by a straight line at which all the refraction is considered to occur.
In each ray diagram in Figure 3.2.39, two rays are drawn from the top A of an object OA. Where these rays intersect after refraction gives the top B of the image IB. The foot I of each image is on the axis since ray OC passes through the lens undeviated.
O
I
B
2F F C
F 2F
image A
Image is between F and 2F, real, inverted, diminished
▲ Figure 3.2.39a Object beyond 2F
2F F C
F 2F
O
I
image A
Image is at 2F, real, inverted, same size B
▲ Figure 3.2.39b Object at 2F
2F F C
F 2F
O A
I
B image Image is beyond 2F, real, inverted, enlarged
▲ Figure 3.2.39c Object between 2F and F
In Figure 3.2.39d, the broken rays, and the image, are virtual. The virtual image is formed by extrapolating diverging rays backwards and cannot be formed on a screen. In all parts of Figure 3.2.39, the lens is a converging lens.
F O C F
B
A
Image is behind object, virtual, upright, larger I
▲ Figure 3.2.39d Object between F and C
Going further
Power of a lens
The shorter the focal length of a lens, the stronger it is, i.e. the more it converges or diverges a beam of light. We define the power of a lens, P, to be 1/focal length of the lens, where the focal length is measured in metres:
P f
= 1
Magnifying glass
The apparent size of an object depends on its actual size and on its distance from the eye. The sleepers on a railway track are all the same length but those nearby seem longer. This is because they enclose a larger angle at your eye than more distant ones:
their image on the retina is larger, so making them appear bigger.
A converging lens gives an enlarged, upright, virtual image of an object placed between the lens and its principal focus F (Figure 3.2.40a opposite). It acts as a magnifying glass since the angle ß made at the eye by the image, formed at the near point (see next section), is greater than the angle α made by the object when it is viewed directly at the near point without the magnifying glass (Figure 3.2.40b).
3.2.3 Thin lenses
F F image
converging lens
object
β
a
object α
b
▲ Figure 3.2.40 Magnification by a converging lens:
angle β is larger than angle α.
The fatter (more curved) a converging lens is, the shorter its focal length and the more it magnifies.
Too much curvature, however, distorts the image.
Magnification
The linear magnification of an image is defined as the ratio of image length to object length, and calculated using the equationis given by
=
linear magnification image length object length
Key definition
Linear magnification the ratio of image length to object length
Spectacles
From the ray diagrams shown in Figure 3.2.39 (opposite) we would expect that the converging lens in the eye will form a real inverted image on the retina as shown in Figure 3.2.41. Since an object normally appears upright, the brain must invert the image.
eye
inverted image object
retina of eye
▲ Figure 3.2.41 Inverted image on the retina
The average adult eye can focus objects comfortably from about 25 cm (the near point) to infinity (the far point). Your near point may be less than 25 cm; it gets further away with age.
Short sight
A short-sighted person sees near objects clearly but distant objects appear blurred. The image of a distant object is formed in front of the retina because the eyeball is too long or because the eye lens cannot be made thin enough (Figure 3.2.42a).
The problem is corrected by a diverging spectacle lens (or contact lens) which diverges the light before it enters the eye, to give an image on the retina (Figure 3.2.42b).
from point on distant object
I a
I b
▲ Figure 3.2.42 Short sight and its correction by a diverging lens
Long sight
A long-sighted person sees distant objects clearly but close objects appear blurred. The image of a near object is focused behind the retina because the eyeball is too short or because the eye lens cannot be made thick enough (Figure 3.2.43a). A converging spectacle lens (or contact lens) corrects the problem (Figure 3.2.43b).