G2 OPTICAL INSTRUMENTS
Notes
II. OPTICAL INSTRUMENTS
A. LENSES AND RAY DIAGRAMS
Lens – rounded and polished glass
Light rays from objects change direction when going through a lens
Lenses can converge light or diverge it
Assume all lenses are thin.
Convex vs. concave lenses
Deviation depends on:
1. nglass
2. angle of incidence
3. curvature of the lens
Different kinds of lenses for
different purposes:
TERMS DEFINED:
Principal axis = line going through center of lens at right angle to surface
Converging lens = thicker in the middle than the edges
Focal point (F) = The point on the other side of converging lens where rays come together
Focal length (f) = Distance from the center of the lens to the focal point
Power (p) = Quantization of strength of a lens
units = m-1 = ‘diopters’ (D)
 if rays not parallel to principal axis, they
converge along same vertical plane as F.
Source: Physics for the IB Diploma, 5th Ed, Tsokos
 note f = f’
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THREE POSSIBILITIES for rays through lenses:
Call them rays 1,2,3
Different images depending on
distance between object and lens
Source: Physics for the IB Diploma, 5th Ed, Tsokos
 rays going through F or F’ will emerge on the
other side parallel to one another
DEMO: Different lenses, different
f’s, different p’s
B. REAL AND VIRTUAL IMAGES
Point objects give out light in all directions.
By looking you can tell where the object is.
Different images depending on distance between object and lens
This is the image.
DEFINE: Real Image = the rays
come from the image; actual rays of
light pass through it. DEMO
Can be projected onto a screen.
Source: Physics for the IB Diploma, Hamper
If light passes through a lens, it may appear as if
point object is somewhere else.
DEFINE: Virtual Image = the rays
only appear to come from a point; no
actual rays of light pass through it.
Cannot be projected onto a screen.
DEMO
Most things are not point objects, but
extended objects. Represent by an
arrow usually.
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GRAPHICAL METHODS
CASE 1: Object placed beyond F
Consider object height 1 cm, 10 cm from a lens of focal length 5 cm (hi = 1 cm u = 10 cm, f = 5
cm.)
Draw a ray diagram, with rays 1,2,3:
Source: Physics for the IB Diploma, 5th Ed, Tsokos
Where they meet on the other side, where the image formed! Easy! Image is inverted too.
NOTE: ho = 1 cm, v = 10 cm.
CASE 2: Object placed at F
u = f = 5 cm
What happens? Draw a ray diagram.
No image formed (at infinity).
NOTE: ho = v = infinity
CASE 3: Object placed within F
Source: Physics for the IB Diploma, 5th Ed, Tsokos
hi = 1 cm u = 3.5 cm, f = 5 cm
Refracted rays do not intersect.
When extended backwards, intersect
to form a virtual image.
Image is magnified and upright.
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ALGEBRAIC METHODS
Turns out we can use this equation to find images (do not need to derive).
THIN LENS EQUATION:
MAGNIFICATION EQUATION:
Where: +f for converging lenses
+u always
+v for real images (other side of lens from object)
-v for virtual images (same side of lens as object)
m > 0 for upright images
m<0
for inverted images
|m| > 1 for image larger than object
|m| < 1 for image smaller than object
Source: Physics for the IB Diploma, 5th Ed, Tsokos
EXAMPLE 2
A converging lens has focal length 15 cm. An object is placed 60 cm from the lens. Determine
the image. Solve algebraically and graphically.
[real, 1.3 the size of object, inverted]
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EXAMPLE 3
An object is placed 15 cm in front of a converging lens of focal length 20 cm. Determine the
image algebraically and graphically.
[virtual, 3 times the size of object, upright]
C. MAGNIFYING GLASSES
DEFINE: Near point = closest point on which human eye can focus (25 cm)
DEFINE: Far point = farthest point on which human eye can focus (infinity)
Objects far away appear smaller; closer appear bigger.
If we want to see an object clearly, it needs to be close (but 25 cm is the limit!)
THEREFORE, the best magnifying glass would create a virtual image with a v = -25 cm.
Assuming θ small, θ ≈ tan θ ≈
Solving, with v = -25….
th
Source: Physics for the IB Diploma, 5 Ed, Tsokos
or
and into
…… gives angular magnification
Assume lens is close to the eye.
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D. MICROSCOPES
Source: Physics for the IB Diploma, 5th Ed, Tsokos
Now use two converging lenses to
enhance the magnification.
Object placed beyond F of objective
(first lens)
Real, inverted image becomes
object for second lens
Enlarged, virtual final image at
infinity
Manufacturers make L = 16 cm =
tube length
If image of objective lens formed past the fo ≠ 16 cm, then
EXAMPLE 4
A microscope has an objective of focal length 0.500 cm and an eyepiece of focal length 3.00
cm. What is the magnification of the microscope?
[-267]
E. TELESCOPES
GOAL: To allow observation of large objects that are far away (stars, etc).
Angle at which star observed through telescope > angle at which star observed with naked eye
Uses two converging lenses to
enhance the magnification.
Object far away; image produced
by objective lens at fo.
Real, inverted image becomes
object for second lens
Enlarged, virtual final image at
infinity
Source: Physics for the IB Diploma, 5th Ed, Tsokos
Distance between lenses = fo + fe
and
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EXAMPLE 5
A refracting telescope has a magnification of 70.0 and the two lenses are 60.0 cm apart when
adjusted for a relaxed eye. What are the focal lengths of the lenses?
[fe = 0.845 cm, fo = 59.2 cm]
F. LENS ABERRATIONS
Aberrations cause an image to be less than perfect (blurry or distorted).
Very common!
Two types:
1. Spherical: rays that enter lens far from
the principal axis have different focal
length from rays entering near the axis.
Because the thickness of the lens
varies.
Magnification also varies, image is
blurry.
Can be reduced by using a lens with smaller diameter…. But this reduces intensity, so
dimmer image.
Produces rainbow effect around edges of image.
Can be reduced by using a combination of lenses
(diverging and converging together)
Source: Physics for the IB Diploma, 5th Ed, Tsokos
2. Chromatic: lens has different refractive indices for
different wavelengths. So different f for each λ.
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