Chapter 25 Optical Instruments 2017 A Dzyubenko Optical

Chapter 25 Optical Instruments © 2017 A. Dzyubenko

Optical Instruments • Analysis generally involves the laws of reflection and refraction: realm of Geometric optics • To explain certain phenomena, the wave nature of light must be used

The Camera • Is an optical instrument • Components: – Opaque, light-tight box – Converging lens I Object O • Produces a real image – CCD (or Film) behind the lens • Receives the image digital analog Real Inverted M<0 I smaller than O |M | < 1

Digital Camera • Image is formed on an electric device CCD: Charge-Coupled Device CMOS: Complementary Metal-Oxide Semiconductor • Both convert the image into digital form • The image can be stored in the camera’s memory

Camera Operation • Proper focusing leads to sharp images The lens-to-film distance q depends on: the object distance p and on the focal length f of the lens • The shutter is a mechanical device that is opened for selected time intervals • Most cameras have an aperture of adjustable diameter D to control the intensity of the light reaching the film Small-diameter aperture: only light from the central portion reaches the film => spherical aberration is minimized

Camera Operation, Intensity • Light intensity: the rate at which energy is received by the film per unit area • The intensity is proportional to the area of the lens, ~ D 2 • The brightness of the image formed on the film depends on the light intensity – Depends on both the focal length f ~1/f and the diameter of the lens D: Intensity 2

Camera, f-numbers • The ƒ-number of a camera is the ratio of the focal length of the lens to its diameter f: D f ƒ-number = f/D The ƒ-number is given a description of the lens “speed” • A lens with a low f-number is a “fast” lens Can take pictures in low-light conditions QQz: this lens, fast or slow?

Camera, f-numbers, Cont. • The lowest ƒ-number setting: the aperture wide open, the maximum possible lens area in use • Simple “point-and-shoot” cameras: a fixed focal length and a fixed aperture size, with an ƒ-number of about 11 The high value of ƒ allows for a large depth-of-field => no need to focus the camera => no good pictures in low-light conditions

Bokeh small depth-of-field

The Eye • The normal eye focuses light and produces a sharp image • Essential parts of the eye: Cornea – light passes through this transparent structure Aqueous Humor – clear liquid behind the cornea • The pupil A variable aperture An opening in the iris • The crystalline lens Most of the refraction takes place at the outer surface of the eye, where the cornea is covered with a film of tears

The Eyes – Parts, Cont. • The iris is the colored portion of the eye – It is a muscular diaphragm that controls pupil size – Regulates the amount of light entering the eye by dilating the pupil in low-light conditions and contracting the pupil in high-light conditions – The f-number of the eye is from about 2. 8 to 16

The Eye – Operation • The cornea-lens system focuses light onto the back surface of the eye, called the retina – The retina contains receptors of two types, rods and cones – These structures send impulses via the optic nerve to the brain The brain converts these impulses into our conscious view of the world

The Eye – Operation, Cont. • Rods and Cones – Chemically adjust their sensitivity to light conditions • Adjustment takes about 15 minutes • This phenomena is “getting used to the dark” • Accommodation – The eye focuses on an object by varying the shape of the crystalline lens – How? The ciliary muscle, situated in a circle around the rim of the lens – Thin filaments, called Zonules, run from this muscle to the edge of the lens low light color vision

The Eye – Focusing • The eye can focus on a distant object The ciliary muscle is relaxed, the zonules tighten This causes the lens to flatten, increasing its focal length f For an object at infinity, f is equal to the fixed distance between lens and retina, about 1. 7 cm • The eye can focus on near objects: The ciliary muscles tense, this relaxes the zonules The lens bulges a bit and the focal length f decreases The image is focused on the retina

The Eye – Near and Far Points • The near point is the closest distance for which the eye can accommodate Average is about 25 cm and increases with age • The far point of the eye: the largest distance for which the lens of the relaxed eye can focus light on the retina Normal vision has a far point of infinity, Eyes may suffer a mismatch between: the focusing power of the lens-cornea system and the length of the eye d,

Conditions of the Eye • A mismatch between the focusing power of the lens-cornea system and the length of the eye, d d • Eyes may be Nearsighted Light rays reach the retina after they converge to form an image Farsighted Light rays reach the retina before they converge to form an image

Farsightedness Light rays reach the retina before they converge to form an image • Also called hyperopia • The image focuses behind the retina • Can usually see far away objects clearly, but not nearby objects

Correcting Farsightedness • A converging lens placed in front of the eye can correct the condition • The lens refracts the incoming rays more toward the principle axis before entering the eye – This allows the rays to converge and focus on the retina

Nearsightedness Light rays reach the retina after they converge to form an image • Also called myopia • In axial myopia: the lens is too far from the retina • In refractive myopia: the lens-cornea system is too powerful

Correcting Nearsightedness • A diverging lens can be used to correct the condition. • The lens refracts the rays away from the principle axis before they enter the eye – This allows the rays to focus on the retina.

Presbyopia and Astigmatism • Presbyopia is due to a reduction in accommodation ability: The cornea and lens do not have sufficient focusing power to bring nearby objects into focus on the retina Condition can be corrected with converging lenses • In Astigmatism, the light from a point source produces a line image on the retina Produced when either the cornea or the lens or both are not perfectly symmetric Can be corrected with lenses having different curvatures in two mutually perpendicular directions

Diopters • Optometrists and ophthalmologists usually prescribe lenses measured in diopters The power of a lens in diopters equals the inverse of the focal length in meters diopters focal length in meters Farsighted? Nearsighted?

Simple Magnifier • A simple magnifier consists of a single converging lens This device • … is used to increase the apparent size of an object • The size of an image formed on the retina depends on the angle subtended by the eye

The Size of a Magnified Image • When an object is placed at the near point, the angle subtended is θo – The near point is about • When the object is placed near the focal point of a converging lens, the lens forms a virtual, upright, and enlarged image h’

Angular Magnification, m • Angular magnification is defined as • The angular magnification is at a maximum when the image formed by the lens is at the near point of the eye: q = - 25 cm Calculations give lens held close to the eye

Magnification m by a Lens • With a single lens, it is possible to achieve angular magnification up to about m = 4 without serious aberrations • With multiple lenses, magnifications of up to about m = 20 can be achieved – The multiple lenses can correct for aberrations

Compound Microscope • A compound microscope consists of two lenses – Gives greater magnification than a single lens – The objective lens has a short focal length, ƒo< 1 cm – The ocular lens (eyepiece) has a focal length, ƒe, of a few cm

Compound Microscope, Cont. • The lenses are separated by a distance L L >> ƒo , ƒe is much greater than either focal length • The approach to analysis is the same as for any two lenses in a row: – The image formed by the first lens becomes the object for the second lens • The image seen by the eye, I 2, is virtual, inverted and very much enlarged

Magnifications of the Compound Microscope • The lateral magnification of the microscope is • The angular magnification of the eyepiece of the microscope is • The overall magnification of the microscope is the product of the individual magnifications

Other Considerations with a Microscope • The ability of an optical microscope to view an object depends on the size of the object, d, relative to the wavelength λ of the light used to observe it. – Example, you could not observe an atom with visible light: d 0. 1 nm λ 500 nm Electronatomic-forcetunnelingmicroscopy

Telescopes • Two fundamental types of telescopes – Refracting telescope uses a combination of lenses – Reflecting telescope uses a curved mirror and a lens In both types, two optical elements in a row: the image of the first element becomes the object of the second element

Refracting Telescope • The objective forms a real, inverted image I 1 • The image is near the focal point of the eyepiece Fe • The two lenses are separated by the distance ƒo + ƒe about the length of the tube • The eyepiece forms an enlarged, inverted image I 1 of the distant object

Angular Magnification of a Telescope • The angular magnification depends on the focal lengths of the objective and eyepiece: • Angular magnification is only important for observing nearby objects • Very distant objects such as stars still appear as small points of light • Main goal of astronomy telescopes: Collect Light!

Disadvantages of Refracting Telescopes • Large diameters are needed More Light! to study distant objects • Large lenses are difficult and expensive to manufacture • The weight of large lenses leads to sagging which produces aberrations

Reflecting Telescope • Helps overcome some of the disadvantages of refracting telescopes – Replaces the objective lens with a mirror – The mirror is often parabolic to overcome spherical aberrations • In addition, the light never passes through glass (except a small eyepiece) – Reduced chromatic aberrations

Reflecting Telescope, Newtonian Focus • The incoming rays are reflected from the mirror and converge toward point A – At A, a photographic plate or other detector can be placed • A small flat mirror, M, reflects the light toward an opening in the side and passes into an eyepiece

Examples of Telescopes • Reflecting Telescopes Largest in the world are D= 10 m Keck telescopes on Mauna Kea in Hawaii altitude 4145 m • Refracting Telescopes Largest in the world is Yerkes Observatory in Wisconsin • Has a 1 m diameter

The Hubble Space Telescope • D = 2. 4 -meter observe in the near-UV, visible, and near-IR spectra • Enables us to see deep into space • And further back in time! Its scientific successor is scheduled to be launched in 2018

The Radio. Astron, “biggest-ever” telescope • a Russian orbital D = 10 -meter parabolic • Collecting data on clouds of water molecules found in the discs of galaxies

Resolution • The ability of an optical system to distinguish between closely spaced objects is limited due to the wave nature of light • Two sources of light are close together, but are non-coherent sources • Because of diffraction, the individual images consist of bright central regions flanked by weaker bright and dark rings

Rayleigh’s Criterion • If the two sources are separated so that their central maxima do not overlap, their images are said to be resolved • The limiting condition for resolution is Rayleigh’s Criterion – When the central maximum of one image falls on the first minimum of another image, they images are said to be just resolved

Just Resolved • If viewed through a slit of width a, and applying Rayleigh’s criterion, the limiting angle of resolution is • For the images to be resolved, the angle subtended by the two sources at the slit must be greater than θmin

Barely Resolved (Left) and Not Resolved (Right)

Resolution with Circular Apertures • The diffraction pattern of a circular aperture consists of a central circular bright region surrounded by progressively fainter rings • The limiting angle of resolution depends on the diameter, D, of the aperture

Resolving Power of a Diffraction Grating • If λ 1 and λ 2 are nearly equal wavelengths between which the grating spectrometer can just barely distinguish, the resolving power, R, of the grating is • A grating with a high resolving power can distinguish small differences in wavelength

Resolving Power of a Diffraction Grating, Cont. • The resolving power increases with order number R = Nm • N is the number of lines illuminated • m is the order number No wavelengths are distinguishable for the zeroth-order maximum: • m = 0 so R = 0

Michelson Interferometer • An optical instrument that has great scientific importance • It splits a beam of light into two parts and then recombines them to form an interference pattern – It is used to make accurate length measurements

Michelson Interferometer, Schematic • A beam of light provided by a monochromatic source is split into two rays by a partially silvered mirror M • One ray is reflected to M 1 and the other transmitted to M 2 • After reflecting, the rays combine to form an interference pattern • The glass plate ensures both rays travel the same distance through glass

Measurements with a Michelson Interferometer • The interference pattern for the two rays is determined by the difference in their path lengths • When M 1 is moved a distance of λ/4, successive light and dark fringes are formed – This change in a fringe from light to dark is called fringe shift • The wavelength can be measured by counting the number of fringe shifts for a measured displacement of M • If the wavelength is accurately known, the mirror displacement can be determined to within a fraction of the wavelength