Download Convex Lenses and Mirrors

Physics 1 – Convex Lenses and Mirrors
CoNVEX LENSES AND MIRRORS
Aims
 To correctly setup an optical bench.
 To study how images are formed by simple convex mirrors and lenses.
 To make measurements of object distances, image distances and focal lengths of
convex mirrors and lenses.
 To draw ray diagrams, with principle rays, for both experimental situations.
Introduction
In this experimental tutorial you will first attempt a question which tests your
knowledge and ability to draw principle ray diagrams concerning convex mirrors and
lenses. Then you will perform the necessary experimental procedures to obtain
measurements that should verify theoretical predictions.
Measuring distances
To measure distances accurately on an optical bench you should use a Vertex Pointer.
For example to measure the distance between A and B on an optical bench, follow
these steps:
A
Place the pointer with its left point touching
A. Read the position of the pointer holder by
using the scribe mark on the Perspex tab
against the metre scale on the optical bench.
B
Place the pointer with its right point touching
B. Read the position of the holder as above.
C
The distance required is equal to the
displacement of the pointer holder plus the
length of the vertex pointer.
A
B
Figure 1
Part 1: Tutorial Question (10 mins)
A biconvex lens is placed on an optical bench with an object positioned on the left
hand side and a plane mirror positioned on the right hand side. They are aligned such
that an image is formed in the object plane. The separation between the object and
lens is found to be exactly 50cm.
1.1
Draw a principal ray diagram of the above setup.
1.2
What is the focal length and the power of the lens ?
Part 2: Finding the focal length and power of a convex lens (10 mins)
You will now setup the optical bench with an object (triangular light source), a
converging lens and a plane mirror to demonstrate a method for calculating the focal
length of the lens. You will then be able to calculate the power of the lens.
1
Physics 1 – Convex Lenses and Mirrors
 Use the illuminated triangle in the lamp screen as an object and place it over the
optical bench at one end.
 Mount a convex lens in the lens holder and screw this into place in the saddle on
the optical bench, near the object.
 Gradually move the saddle along the optical bench, away from the object until a
‘faint’ inverted image is formed on the screen in the object plane.
2.1
How has an image formed in the object plane when there is not yet a mirror
placed on the other side of the lens?
 Now place a plane mirror on the optical bench on the opposite side of the lens from
the object.
 Again, gradually move the saddle towards the mirror until you have formed an
inverted bright image in the object plane.
 Use the vertex pointer to accurately determine the separation between the image
and the lens. This is your image distance.
2.2
Calculate the focal length and hence the power of the lens.
Hints:
1 1 1
  , where f = focal length, s = object dist, and s’ = image dist.
f s s'
1
Express f in metres and the power P in dioptres where P  .
f
Part 3: Tutorial Question (15 mins)
A convex lens of focal length 0.24m is placed 0.12m in front of a convex mirror. It is
found that when an object is placed 0.36m in front of the lens it coincides with its own
inverted image formed by the lens and mirror.
3.1
Draw a principle ray diagram of the setup described above.
3.2
Find the focal length of the mirror.
Part 4: Using a convex mirror on the optical bench (15 mins)
In this part you will maintain the object position as in Part 2 and use the same lens as
before. Then you will form an image using a convex mirror and determine its radius
of curvature.
 Place the lens on the optical bench near the object and move it away from the
object until you have passed the first ‘faint’ image formation.
 Replace the plane mirror with the convex mirror and position it on the optical
bench.
 Slide the convex lens towards the mirror or the mirror towards the lens until you
have formed an inverted image in the object plane.
2
Physics 1 – Convex Lenses and Mirrors
 Use the vertex pointer to measure the object distance from the lens then the
separation between the lens and the convex mirror.
4.1
Calculate the radius of curvature of the convex mirror.
4.2
Hence, deduce the focal length and power of the convex mirror.
Part 5: Measurement of focal length by parallax method (Optional)
 Select a convex mirror.
 Use a vertical pin, which should be well illuminated, as an object, placed near the
mirror. A virtual image will be formed behind the mirror.
 Use a second vertical pin, as an image marker, behind the mirror so that while
viewing the image of the object pin in the mirror you can also see the top of the
image marker above the mirror. Use the method of no parallax to set the image
marker at the position where the image appears to be.
5.1
Measure the distance from the mirror to this image pin - this gives a virtual
image distance. Also measure the real object distance. Remember that all
distances should be measured from the vertex of the mirror.
5.2
Calculate the focal length of the convex mirror. What is its sign?
Further work
The following questions are related to the topic covered by this experimental tutorial.
 Exercise book questions L17.
 Mastering Physics: Optics 1 (parts 5 and 6); Optics 2
3
Physics 1 – Convex Lenses and Mirrors
Demonstrators' Answers, Hints, Marking Scheme and Equipment List
1.1
O
F
M
C
1.2
f = 50 cm = 0.5m, therefore P = 1/f = +2 dioptres.
2.1
Total internal reflection.
2.2
for one of the lenses I found f = (28.9-22.5)+20 = 26.4cm, so therefore the
power is P = 1/f = 3.79 dioptres.
3.1
below is not to scale
I2
I1
O
C
S = 0.36 m
0.12 m
Mirror
Lens
3.2
R = 0.60 m
Start with the lens:
f = + 0.24m
S = + 0.36m
 S' = 0.72m
This ray is directed towards the centre of curvature of the mirror, C.
Hence radius of mirror = (0.72 - 0.12)m = 0.60m
Focal length = -0.30m, remembering it is a convex mirror (i.e. f is negative).
4.1
4.2
1 1 1
 
s' f s
1
1
1
1



 s '  66.7cm
s ' 26.4 43.7 66.7
R  s' (mirror/lens separation)  66.7  24.9  41.8cm
2 1
R 41.8
 f  
 20.9cm
R f
2
2
1
1
Power, P =

 4.8 dioptres.
f  0.209
4
Physics 1 – Convex Lenses and Mirrors
5.2
Using their values for image and object distance should yield a realistic focal
length. The focal length should be a negative value because it is a convex
mirror.
Section
1.1
1.2
2.1
2.2
3.1
3.2
4.1
4.2
Discretionary mark
TOTAL
Equipment List
Convex mirror
Convex lens
Plane mirror
Light source
Screen with triangular hole
3 x saddles
3 x holders
5
Mark
1
1
1
1
1
1
1
1
2
10