3B Scientific Optical Bench U, 1200 mm - Manual (Page 17)

17
Experiment 11: Lens formula and magnification,
virtual images
11.1 Equipment:
•
Optical bench U17150
•
Experimental lamp U17140
•
Object holder, shaft-mounted U17000
•
Slide with letter “F” from U17040
•
Concave lens f = +50 mm U17101
•
Concave lens f = +100 mm U17102
•
Concave lens f = +150 mm U17103
•
Diverging lens f = –200 mm U17107
•
Projection screen U17125
•
4 optical riders 75 mm U17160
•
1 optical rider 30 mm U17161
•
Plug-in power supply unit U13900
11.2 Set up
•
Place the experimental lamp vertically on the rail
at the left end position.
•
Set up the converging lens f = +50 mm directly in
front of the lamp.
•
Place the holder with slide at the 0 position, insert-
ing the slide into the holder so that the “F” is up-
side down.
•
Place the concave lenses f = +100 mm and
f = +150 mm at the 5 or 25 cm positions.
•
Set the projection screen up at the 55 cm position.
11.3 Procedure
•
An inverse image of the slide twice the size of the
original is produced at a focal length of 30 cm.
•
According to the lens equation the object distance
then also amounts to 30 cm.
1/b + 1/v = 1/f ; 1/300 + 1/v = 1/150 v = 300 mm
•
We conclude from this that the virtual, non-invert-
ed image of the lens f = 100 mm lies at –5 (i.e 5 cm
left of 0). This image is the same size as the one on
the screen (b = v = 30 cm; b/v = 1). The focal length
is therefore –10 cm (image at –5 , lens at +5). The
object distance amounts to 5 cm. The lens equa-
tion verifies these values:
1/b + 1/v = 1/f ; –1/100 + 1/50 = 1/100 f = 100 mm
The following holds true for the magnification:
b/v = 100/–50 = –2
•
If the diverging lens f = –200 mm is now placed at
the 20 cm position, the concave lens f = +100 mm
and the screen placed at 50, an inverted image is
produced, which is half as large as that on the slide.
According to the lens equation the object distance
to the concave lens is 20 cm
1/v = 1/f – 1/b = 1/10 – 1/20 = 1/20
and the magnification is: b/v = 1.
•
For the diverging lens the image distance is –10 cm,
according to the lens formula, we obtain f = –20 cm
and a magnification b/v = –10/20 = –1/2.
Experiment 12: Lens formula and magnification,
virtual object
12.1 Equipment:
•
Optical bench U17150
•
Experimental lamp U17140
•
Object holder, shaft-mounted U17000
•
Slide with letter “F” from U17040
•
Concave lens f = +50 mm U17101
•
Concave lens f = +100 mm U17102
•
Concave lens f = +150 mm U17103
•
Diverging lens f = –200 mm U17107
•
Projection screen U17125
•
4 Optical rider 75 mm U17160
•
1 Optical rider 30 mm U17161
•
Plug-in power supply unit U13900
12.2 Set up
•
Place the experimental lamp vertically on the rail
and to the far left-hand end.
•
Set condenser lens f = +50 mm directly in front of
the lamp.
•
Set up the holder with slide at the 0 position, there-
by inserting the slide into the holder so that the
letter “F” is upside down.
•
The imaging lens f = +100 mm is placed at the
15 cm position.
•
The projection screen is set up at 45 cm.
12.3 Procedure
•
An inverted image of the slide is produced on the
projection screen that is twice as big as the image
on the slide. This image is used as a virtual image
when another lens is placed between the screen
and the lens.
•
Place the lens f = +150 mm at the 30 cm position
and the screen at the 37.5 cm position.
•
An inverted image of the slide is produced which is
half the size of the image on the slide. The magni-
fication factor now amounts to 0.5. The object dis-
tance is –15 cm, the image distance 7.5 cm. The
lens formula is applicable here too:
1/b + 1/v = 1/f ; 1/75 –1/150 = 1/150 f = 150 mm
•
If the concave lens f = +150 mm is now replaced
by a diverging lens f = –200 mm at the 35 cm posi-
tion, an inverted image is produced on the screen
at the 55 cm position which is four times as large
as the slide for an object distance of –10 cm and
an image distance of 20 cm. The lens formula ver-
ifies these values:
–1/100 + 1/200 = –1/200 f = –200 mm