Chapter 27Chapter 27
Lenses and Optical Lenses and Optical InstrumentsInstruments
Lenses
Converging lens
Diverging lens
Thin LensesThin Lenses
A thin lens consists of a piece of A thin lens consists of a piece of glass or plastic, ground so that each glass or plastic, ground so that each of its two refracting surfaces is a of its two refracting surfaces is a segment of either a sphere or a segment of either a sphere or a planeplane
Lenses are commonly used to form Lenses are commonly used to form images by refraction in optical images by refraction in optical instrumentsinstruments
Thin Lens ShapesThin Lens Shapes
These are These are examples of examples of convergingconverging lenses lenses
They have positive They have positive focal lengthsfocal lengths
They are thickest They are thickest in the middlein the middle
More Thin Lens ShapesMore Thin Lens Shapes
These are These are examples of examples of divergingdiverging lenses lenses
They have They have negative focal negative focal lengthslengths
They are thickest They are thickest at the edgesat the edges
Glass lens (nG = 1.52)
The focal length of a lens is determined by the shape and material of the lens.
Same shape lenses: the higher n, the shorter fLenses with same n: the shorter radius of curvature,
the shorter f
Typical glass, n = 1.52 Polycarbonate, n = 1.59 (high index lens)Higher density plastic, n ≈ 1.7 (ultra-high index lens)
Q.Q. A parallel beam of light is sent through an aquarium. A parallel beam of light is sent through an aquarium. If a convex lens is held in the water, it focuses the beam (……..If a convex lens is held in the water, it focuses the beam (……..……………………. ) than outside the water……………………. ) than outside the water
(a) closer to the lens (b) at the same position as
(c) farther from the lens
nair = 1, nwater = 1.33
Rules for Images
• Trace principle beams considering one end of an object off the optical axis as a point light source.• A beam passing through the focal point runs parallel to the optical axis after a lens. • A beam coming through a lens in parallel to the optical axis passes through the focal point.• A beam running on the optical axis remains on the optical axis.• A beam that pass through the geometrical center of a lens will not be bent.
Find a point where the principle beams or their imaginary extensions converge. That’s where the image of the point source.
two focal points: f1 and f2
Parallel beams: image at infinite!!
Virtual image
Virtual image
Magnifying glass
1/p + 1/q = 1/f
Magnification, M = -q/p
Negative M means that the image is upside-down.
For real images, q > 0 and M < 0 (upside-down).
Lens equation and magnification
1/p + 1/q = 1/f
M = -q/p
This eq. is exactly the same as the mirror eq. Now let’s think about the sign.
positivepositive negativenegative
pp real object real object imaginary objectimaginary object
(multiple lenses)(multiple lenses)
qq real imagereal image
(opposite side of object)(opposite side of object)imaginary imageimaginary image
(same side of object)(same side of object)
ff for converging lensfor converging lens for diverging lensfor diverging lens
MM erect imageerect image inverted imageinverted image
two focal points: f1 and f2
Parallel beams: image at infinite!!
1/p + 1/q = 1/f1/2f + 1/q = 1/f1/q = 1/2f
M = -q/p = -1
1/p + 1/q = 1/f1/f + 1/q = 1/f1/q = 0 q = infinite
Virtual image
Virtual image
Magnifying glass
1/p + 1/q = 1/f2/f + 1/q = 1/f1/q = -1/f
M = -(-f)/(f/2) = 2
Ex. 27.1 A thin converging lens has a focal length of 20 cm.An object is placed 30 cm from the lens. Find the image Distance, the character of image, and magnification.
positive f
f = 20, p = 30
1/q = 1/f – 1/p = 1/20 – 1/30 = 1/60
q = 60
M = -q/p = -60/30 = -2
real image (opposite side)
< 0 inverted
MagnifierMagnifier Consider small object held in front of eyeConsider small object held in front of eye
• Height Height yy• Makes an angle Makes an angle at given distance from the at given distance from the
eyeeye Goal is to make object “appear bigger”: Goal is to make object “appear bigger”: '' > >
y
MagnifierMagnifier Single converging lensSingle converging lens
• Simple analysis: put eye right behind lensSimple analysis: put eye right behind lens• Put object at focal point and image at infinityPut object at focal point and image at infinity• Angular size of object is Angular size of object is , bigger!, bigger!
Outgoingrays Rays seen coming
from here
ff Image atInfinity
1 1 1
q f p
y
Angular Magnification Angular Magnification (Standard)(Standard)
Without magnifier: 25 cm is closest distance to viewWithout magnifier: 25 cm is closest distance to view• Defined by average near point. Younger people do Defined by average near point. Younger people do
betterbetter tan tan = = yy / 25 / 25
With magnifier: put object at distance With magnifier: put object at distance pp = = ff '' tan tan '' = = yy / / ff
Define “angular magnification” Define “angular magnification” mm = = ' / ' / Note that magnifiers work better for older people because Note that magnifiers work better for older people because
near point is actually > 25cmnear point is actually > 25cm
~y/25’~y/fM= ’/ = 25/f
ExampleExample
Find angular magnification of lens Find angular magnification of lens with with ff = 5 cm = 5 cm
255 Standard
525
1 6 Maximum5
m
m
Eye Glasses
Perfect EyeNearsighted
Nearsighted can be corrected with a diverging lens. A far object can be focused on retina.
Optical Instruments
AA
Farsighted
Power of lens: diopter = 1/f (in m) (+) diopter converging lens (-) diopter diverging lens
Larger diopter Stronger lens (shorter f)
MaterialMaterial nn
CorneaCornea 1.381.38
Aqueous Aqueous HumorHumor
1.33-1.33-1.341.34
LensLens 1.41-1.41-1.451.45
Vitreous Vitreous HumorHumor
1.341.34
AirAir 1.001.00
WaterWater 1.331.33
Combinations of Thin LensesCombinations of Thin Lenses
The image produced by the first lens is The image produced by the first lens is calculated as though the second lens calculated as though the second lens were not presentwere not present
The light then approaches the second The light then approaches the second lens as if it had come from the image of lens as if it had come from the image of the first lensthe first lens
The image of the first lens is treated as The image of the first lens is treated as the object of the second lensthe object of the second lens
The image formed by the second lens is The image formed by the second lens is the final image of the systemthe final image of the system
Combination of Thin Lenses, 2Combination of Thin Lenses, 2
If the image formed by the first lens If the image formed by the first lens lies on the back side of the second lies on the back side of the second lens, then the image is treated at a lens, then the image is treated at a virtual objectvirtual object for the second lens for the second lens• p will be negativep will be negative
The overall The overall magnificationmagnification is the is the product of the magnification of the product of the magnification of the separate lensesseparate lenses