Magnifiers 5.1 Optical Instruments - • We magnify the image a small object by bringing it Polarization close to our eye. • But we cannot bring it closer than the near point. • Optical Instruments • A magnifier can produce a larger image of the – Simple magnifier object at the near point (or farther away) that can be – Compound microscope focused on by the eye. – Telescope • The larger image is due to Angular • Wave optics Magnification –Polarization
Angular size Simple Magnifier A converging lens in combination with the lens of Not to scale the eye forms an image on the retina from an object 25 cm closer than the near point of the eye. unfocused Ignore the distance 25 cm between the lens and the eye θ h P image on The angle θ increases as p decreases retina Virtual image The image size increases formed by magnifier Larger Real image Objects closer than the near point are not in focus.
Angular Magnification Angular magnification The angular magnification is the ratio of θ for the magnified image compared to value of θo for the object at the near point of the eye. (25 cm) θ The angular magnification for the simple m = magnifier can have a range of values θo h’ 25 cm Magnified because the focal length of the eye can virtual object image vary due to accommodation. θ h • f The simplest case is the magnification for 25 cm Unmagnified the relaxed eye. (focused at infinity) h θo
1 Angular magnification
Simple Magnifier 25 cm Simple magnifier. Magnified object
θ h A simple magnifier with a focal length of 5.0 • h cm is used to view an insect. What is the tanθ = f p q = -infinity f angular magnification for a relaxed eye?
25 cm Unmagnified 25cm 25cm h θ m5.0== = o f5.0cm
h h for small angles tan θ ~ θ θ≈ θ≈ f o 25cm θ 25cm m == f is the focal length Angular magnification θ0 f of the lens in cm.
Simple magnifiers. Compound Microscopes.
The angular magnification for a single lens is Magnification by 2 lenses. limited by aberration to about 4. Objective lens – Produces an enlarged Combination lenses can have real image of the object. magnification to about 20. Eyepiece – Used like a simple magnifier to view the image. The net angular magnification of the product of the two magnifications.
Compound microscope Compound microscope
Eyepiece
Objective
Not to scale
The objective lens produces a magnified real image I1 The image is viewed through the eyepiece.
2 Two stages of magnification by 1) objective and 2) eyepiece. Total Magnification is the product
Not to scale
The objective lens produces a magnified real image I1 The image is viewed through the eyepiece. L(25cm) 25cm mMm==−1e q1 L For relaxed eye ff M =− ≈− me = oe o pf f 1o e Magnification increases when fe and fe get smaller.
Magnification Refracting Telescope
A compound microscope has an objective Two lenses lens and eyepiece with a focal lengths of Objective lens – produces a reduced image 1.5 cm and 2.0 cm respectively. The of a distant object near the focal point. microscope is 20 cm long. Find the angular magnification Eyepiece – used to magnify the image.
L (25cm) 20 (25cm) m=− =− =− 167 ffoe 1.52.0
Angular magnification - ratio of the focal length of Telescope the objective and the eyepiece The Hubble space telescope has an objective mirror with a focal length of 57.8 m viewed with optics equivalent to an eyepiece with a focal length of 7.2x10-3m h' θ= What is the angular magnification? fe h' fo 57.8 3 θ=o m8.0x10==−3 = fo f7.2x10e
θ f focus at infinity Angular magnification m ==o θoef
3 Hubble Telescope Image of M100 Spiral Galaxy (NASA) Limits to magnification
• For refracting optics there are problems of chromatic and spherical aberration. • Problems in precision in constructing the refracting and reflecting surfaces. • Diffraction – A basic problems having to do with the wave nature of light (discussed next week)
Wave Properties of Light
Polarization Wave optics or Physical optics is the study of the wave properties of light. Polarized Light Some wave properties are: Polarization by absorption Interference, diffraction, and polarization. Polarization by reflection These properties have useful applications in Polarization by scattering optical devices such as compact discs, diffraction gratings, polarizers.
Polarization Light is a transverse wave
• Polarized light has it E field along one direction. • Light can be polarized by several different processes – Absorption – Polaroid filter – Reflection – Brewster’s angle – Scattering – Light from the sky • Polarized light has many applications – Polaroid sunglasses, Polarization microscopy, liquid crystal display. A plane wave with Electric field in the y direction
There is no E field in the direction of propagation
4 Polarized and un-polarized light Polarization by absorption
Oriented molecules Ey absorb light with E along y direction
Ez un-polarized
Ez Polaroid film polarized
Unpolarized Light Polarized Light for an ideal polarizer the intensity 1 has E field in a II= has E field at any instant is reduced by 1/2 polarized2 unpolarized can have E in any direction. certain direction
Polarized light passing through a Polarized light passing though polarizer at angle θ a polarizer The angle of θ parallel component polarization changes Eo Eo cosθ transmitted
Eo cosθ
Esinθ
Io 2 But I ∝ E2 Io cos θ Decrease in intensity when polarized light passes Therefore transmitted intensity through a polarizer I = I cos2θ Law of Malus o 2 I= Io cos θ
Two polarizers Example
2 I=Io cos θ Un-polarized light is incident upon two polarizers that have their polarization axes at an angle of o 45 . If the incident light intensity is Iowhat is the final intensity? 45o
I o Io I o cos2 θ 2 o 2 θ=0 θ=45 θ=90o IIIooo2 ⎛⎞1 “Crossed-polarizers” I ===cos 45 ⎜⎟ 2224⎝⎠
5 Polarization by reflection Polarization by reflection Un-polarized light can be polarized by
reflection at a specific polarization angle θp E is (Brewster’s angle) ⊥to plane of incidence
This E θ θ Fully polarized Un-polarized p p component n1 is absent
o 90 n2 n 2 θ2 tanθp = n1 Reflected beam is Reflected beam is Partially polarized Fully polarized
Example Polarization by reflection Suppose you wanted to have fully polarized light by reflection at the air water interface. What conditions would you use? What would be the direction of the polarized E field? Angle of incidence equal to the polarizing angle θp n1 =1.00
• n2 • tanθ=p = 1.333 n1 n =1.333 o 2 θ=p 53
no filter polarizing filter E would be ⊥ to the plane of incidence. The reflected light is polarized -
Polarization by scattering Polarization of light by air Plane wave has no E field in the direction of propagation Scattering particle has oscillations partially polarized in the plane ⊥ to the direction of propagation
scattered light is partially polarized with E field ⊥ to observer the direction of propagation of the incident light
6 Polarization of scattered light Applications- Crossed Polarizers Light from the sky is partially polarized
Crossed polarizers used to detect materials that rotate no filter polarizing filter the plane of polarized light (optically active materials) including many biological materials and materials under mechanical stress
Applications – Liquid crystal display (LCD)
Oriented molecules rotate the plane of the polarized light
Light
When an electric field is applied the molecules reorient so that the Dark light is not rotated.
LCD displays
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