Phy Ph s y 102 Lecture Lectur 21 Optical instruments 1

Transcription

1 Phys 102 Lecture 21 Optical instruments 1

2 Today we will... Learn how combinations of lenses form images Thin lens equation & magnification Learn about the compound microscope Eyepiece & objective Total magnification Learn about limits to resolution Spherical & chromatic aberrations Dispersion Phys. 102, Lecture 21, Slide 2

3 CheckPoint : multiple lenses Image of first lens becomes object for second lens, etc... p.a. Lens 1 Lens 2 DEMO Phys. 102, Lecture 21, Slide 3

4 Calculation: final image location Determine the final image location for the 2 lens system s = 18 cm d o,2 d i,2 p.a. d o,11 d i,11 Lens 1 Lens 2 3 cm 3 cm = d f d i,1 1 o, = d f d i,2 2 o,2 Phys. 102, Lecture 21, Slide 4

5 Calculation: final magnification Determine the final image size for the 2 lens system h o,1 h i,2 p.a. Lens 1 Lens 2 3 cm 3 cm mtot = mm 1 2 hi,2 = mtotho,2 Phys. 102, Lecture 21, Slide 5

6 ACT: CheckPoint 1.3 Now, the second converging lens is placed to the left of the first lens image. p.a. Lens 1 2 Which statement is true? A. Lens 2 has no object B. Lens 2 has a real object C. Lens 2 has a virtual object Phys. 102, Lecture 21, Slide 6

7 ACT: CheckPoint 1.4 Now, the second converging lens is placed to the left of the first lens image. p.a. Lens 1 2 What is the image formed from lens 2? A. There is no image B. Real C. Virtual Phys. 102, Lecture 21, Slide 7

8 Lens combination: summary... f... d o,1 1 d i,1 1 d o,2 2 d i,2 2 Image of first lens becomes object of second lens,... m tot = mm m d o = distance object is from lens: d i = distance image is from lens: > 0: real object (before lens) > 0: real image (after lens) < 0: virtual object (after lens) <0: virtual image (before lens) f = focal length lens: > 0: converging lens < 0: diverging lens > 0: converging lens Watch your signs! Phys. 102, Lecture 21, Slide 10

9 Compound microscope A compound microscope is made up of two converging lenses Eyepiece (ocular) Acts as a magnifying glass f e Body tube Tube length L = distance between focal points Objective Creates real, enlarged image of sample object Sample L f o f o Phys. 102, Lecture 21, Slide 11

10 Microscope ray diagram Total image magnification: M = M m = tot e o d near f e L f o Eyepiece (ocular) Objective Sample f e L f o f o Eyepiece creates virtual, upright image at M e = d near f e Recall Lect. 20 Object just past objective focal pt. creates real, inverted image at eyepiece focal pt. d = f 1 i i m o o d d o di = = d o L+ o = + fo L f o f m o Phys. 102, Lecture 21, Slide 12

11 ACT: Microscope eyepiece The magnification written on a microscope eyepiece assumes the user has normal adult vision Magnification What is the focal length of a 10 eyepiece? A. f e = 2.5 cm B. f e = 10 cm C. f e = 25 cm Phys. 102, Lecture 21, Slide 13

12 ACT: Microscope objective A standard biological microscope has a 160 mm tube length and is equipped with a 40 objective Tube length Magnification What is the focal length of the objective? A. f o = 4 mm B. f o = 8 mm C. f o = 16 mm Phys. 102, Lecture 21, Slide 14

13 Modern microscope objectives Most modern objectives are infinity corrected Finite system Infinity system Eyepiece Intermediate image Objective Extra tube lens creates intermediate image Objective creates image at ; rays are Phys. 102, Lecture 21, Slide 15

14 Calculation: Angular size A microscope has a 10 eyepiece and a 60 objective. How much larger does the microscope imageappear appear to our eyes? M = Mm tot e o At a near pt. o5 cm, a 2 μm bacterium has angular size to an unaided eye of: In the microscope the angular size is: Bacillus subtilis Phys. 102, Lecture 21, Slide 16

15 Aberrations Aberrations are imperfections relative to ideal lens Spherical: rays hitting lens at different points focus differently Chromatic: rays of different color focus differently Hubble space telescope White light Where do chromatic aberrations come from? Phys. 102, Lecture 21, Slide 17

16 Dispersion The index of refraction n depends on λ In glass, n blue > n green > n red In prism, θ blue < θ green < θ red θ red DEMO θ i θ green White light θ blue Prism Blue light gets dfl deflected tdmore n i sin θ i = n sin θ = n sin θ = n sin θ blue blue green green red red Phys. 102, Lecture 21, Slide 18

17 CheckPoint 2.1: Rainbows Dispersion in water droplets create rainbows θ i θ red Sunlight θ blue θ green Blue light gets deflected more In water, n blue > n green > n red Phys. 102, Lecture 21, Slide 19

18 Double rainbow LIKE SO! Second rainbow created from second reflection inside droplet. Second reflection reverses pattern Double rainbow Phys. 102, Lecture 21, Slide 20

19 ACT: Dispersion A diverging lens made of flint glass has n red = 1.57, n blue = Parallel rays of white light are incident on the lens. Which diagram best represents how light is transmitted? A. B. C.? Phys. 102, Lecture 21, Slide 21

20 Ultimate limit of resolution One can play clever tricks with combinations of lenses to compensate for spherical and chromaticaberrations aberrations Ultimately, even withideal ideal lenses resolution of light microscope is limited to ~λ of light (~500 nm) We won t understand why using ray picture of light; we have to treat light as a wave again Bacillus subtilis Ray optics works for objects >> λ Next two lectures! Phys. 102, Lecture 21, Slide 22

21 Summary of today s lecture Combinations of lenses: Image of first lens is object of second lens... The compound microscope Objective forms real image at focal pt. of eyepiece Eyepiece forms virtual image at Limits to resolution Spherical & chromatic aberrations Dispersion Diffraction limit next week! Watch signs! Phys. 102, Lecture 21, Slide 23