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Optical instruments PHY232 Remco Zegers [email protected] Room W109 – cyclotron building http://www.nscl.msu.edu/~zegers/phy232.html optical instruments Most optical instruments involve just the laws of reflection and refraction – microscope, telescope etc some optical instruments make use of the wave-nature of light, such as the interferometer In this chapter we consider some optical instruments, starting with the eye PHY232 - Remco Zegers - optical instruments 2 the eye the eye essentially consists of a lens that focuses light on the retina. The ciliary muscles are used to change the curvature of the lens and hence the focal length. PHY232 - Remco Zegers - optical instruments 3 the eye II when the ciliary muscles are relaxed, an object at infinity is focused onto the retina. The focal length is about 1.7 cm. optometrists define the power P of a lens in terms of diopters D=1/f (f in m, D in diopters 1/m) the typical eye has a power of 1/0.017 m=59 diopters PHY232 - Remco Zegers - optical instruments 4 the far-point The largest distance that can clearly be seen is called the far-point FP. a good human eye can visualize objects that are extremely far away (moon/stars) and the far point is then close to infinity. PHY232 - Remco Zegers - optical instruments 5 nearsightedness (myopia) In case of nearsightedness, the far-point is much smaller than infinity for example because the eyeball is elongated. on object placed at infinity is focused in front of the retina. this can be corrected using a diverging lens… PHY232 - Remco Zegers - optical instruments 6 example A person cannot see objects clearly that are more than 50 cm away from his eye. An optometrist therefore prescribes glasses to solve the problem. What should the power of the lens be (in diopters) to solve the problem? You can ignore the distance between the glasses and the eye lens. without glasses - - - 20/20 vision: you can see on the chart what average people can see from 20 feet PHY232 - Remco Zegers - optical instruments 7 the near point The near-point is the closest distance in front the eye that a person is capable of focusing light on the retina the near-point for a normal person is about 25 cm, making it hard to focus an object closer to you eyes than that. PHY232 - Remco Zegers - optical instruments 8 farsightedness (hyperopia) happens when the nearpoint is much larger than 25 cm. it becomes hard to see objects nearby since the eye muscles cannot accommodate it. it can be corrected using a converging lens (reading glasses) PHY232 - Remco Zegers - optical instruments 9 example a person suffering from hyperopia has a near point of 1 m. The optometrist has to prescribe a lens of what power to put the near point back at 25 cm? PHY232 - Remco Zegers - optical instruments 10 question a person has a far-point of 1 m and a near point of 75 cm. In order to help this person see objects that are far away and allows him/her to read a book… a) bi-focal glasses are needed, which are partly diverging and partly converging b) glasses are needed that bring the far-point and the near-point together c) an operation is needed to solve at least one of the problems so that the other can be solved with glasses PHY232 - Remco Zegers - optical instruments 11 lon-capa do questions 10,11 from set 9 PHY232 - Remco Zegers - optical instruments 12 simple magnifier 0 h eye NP h’ h p f q the best result is obtained if the image is at infinity (eye relaxed). to do so p=f and m=NP/f PHY232 - Remco Zegers normal eye cannot focus if the object distance < near point (NP) therefore, the maximum subtended angle equals: 0=h/NP=h/(25 cm) (assumed that tan= : small if we put the same object in front of a converging lens with p<f, a virtual upright image is created 1/p+1/q=1/f with p<f q=pf/(p-f) with p<f so q: negative M=himage/hobject =-q/p=-f/|f-p| with p<f so M>1 maximum subtended angle now equals: I=h’/q=h/p angular magnification m=I/0 m=I/0=(h/p)/(h/NP)=NP/p - optical instruments 13 example A lens with f=10 cm is used as a magnifier. What is the angular magnification if the image if formed at the near point? What is the angular magnification if the eye is relaxed (image at infinity?) PHY232 - Remco Zegers - optical instruments 14 the microscope… L …uses two converging lenses with focal lengths f1 and f2 with f2>f1 moreover, L>>f2 For lens 1: p1 is chosen such that q1~L (image 1 will appear just within F2) This happens when p1~f1 so: M1=-q1/p1=-L/f1 Lens two then acts as a magnifying glass with m2=NP/f2=25/f2 The magnifying power is defined as m=M1m2=(-L/f1)(25/f2)=-25L/(f1f2) (all units in cm), usually written as: m=-25L/(fOfe) (inverted!) with O for objective and e for eyepiece PHY232 - Remco Zegers - optical instruments 15 example A red blood cell has a size of about 7x10-6 m. A microscope is used to visualize it. The microscope has L=30cm, f0=1 cm, fe=0.5 cm. How large is the cell when seen through the microscope? PHY232 - Remco Zegers - optical instruments 16 L a telescope size of image of objective lens: hi e o a telescope is very similar to a microscope except that the lenses are slightly differently configured: light comes in (from a star) almost parallel. It is focused at the focus point fo of the first converging (objective) lens. this image becomes the object for the second converging (eyepiece) lens and is place just at the focal length fe of that lens. tan(o)o=hi/fo tan(e)e=hi/fe magnifying power m= e/o=fo/fe note L=f0+fe PHY232 - Remco Zegers - optical instruments 17 example A telescope has two lenses which are 92 cm apart from eachother. The angular magnification of the telescope is 45. What are the focal lengths of the objective and eyepiece lens? PHY232 - Remco Zegers - optical instruments 18 loncapa do problem 12 from lon-capa 9 PHY232 - Remco Zegers - optical instruments 19 resolution resolution: the ability of an optical system to distinguish between two closely spaced objects resolution is limited by the wave nature of light: when light passes through a slit, it is diffracted and thus smeared out. if the angular separation becomes two small, objects become hard to distinguish PHY232 - Remco Zegers - optical instruments 20 rayleigh’s criterion two images are just resolved if rayleigh’s criterion is fulfilled. Rayleigh’s criterion: the central maximum of image A false into the first minimum of image B first diffraction minimum: sin=/a with A the slitwidth images separated by a minimum angle min=/a can just be resolved if the aperture is circular with diameter D: min=1.22/D PHY232 - Remco Zegers - optical instruments 21 min=1.22/D question a binary star system consists of two stars that are rotating around each other. Because of there closeness they are hard to separate. A color filter can be used to improve the separation. Is it better to use blue or red to make a picture that best separates the stars? a) Blue b) Red c) doesn’t matter PHY232 - Remco Zegers - optical instruments 22 lon-capa do problem 13 from lon-capa 9 use min=1.22/D distance earth moon is 3.84E+8 m how to calculate min? you can use tan= (radians) use a wavelength of 550 nm PHY232 - Remco Zegers - optical instruments 23 The Michelson Interferometer moveable 1) 2) 3) 4) 5) 6) monochromatic light is incident on mirror light travels to moveable mirror and is… 1 reflected some light is also passed through and is … reflected beam 3) and 5) interfere and make an interference pattern 7) by moving the moveable mirror, the path length difference can be varied PHY232 - Remco Zegers - optical instruments 3 2 5 6 4 24 Michelson interferometer moveable 3 2 5 1 6 4 the compensator servers to make sure that the light going to either branch travels the same distance through the glass. The path length difference D=2d23-2d45 If the movable mirror moves by /2, D changes by and the interference pattern is shifted by 1 fringe. Insertion of a material with index of refraction n in path 2-3 will also make a path length difference, and by observing the change in the interference pattern, one could determine n more about this in the last week’s lecture on relativity… PHY232 - Remco Zegers - optical instruments 25