Observational Instruments & Methods 2023-24 Fall PDF

Type equation here. ÖNEMLİ UYARI: Bu sunum İ.Ü. İstanbul Fen Fakültesi Lisans öğrencilerinin eğitimlerine ücretsiz katkı sağlamak amaçlı hazırlanmış olup, bilimsel kaynak olarak gösterilemez, ücretlendirilemez, izinsiz kaydedilemez, kullanılamaz, çoğaltılamaz ve ticari bir ürün haline dönüştürülemez...

Type equation here. ÖNEMLİ UYARI: Bu sunum İ.Ü. İstanbul Fen Fakültesi Lisans öğrencilerinin eğitimlerine ücretsiz katkı sağlamak amaçlı hazırlanmış olup, bilimsel kaynak olarak gösterilemez, ücretlendirilemez, izinsiz kaydedilemez, kullanılamaz, çoğaltılamaz ve ticari bir ürün haline dönüştürülemez. İSTAN B U L ÜNİVERSİTESİ OBSERVATIONAL INSTRUMENTS & METHODS 2023-24 FALL CLASS CODE: ASUB3229 (STUDENTS ENROLLED AFTER 2017-2018 EDUCATION SEASON) CLASS CODE: ASUB4195 (STUDENTS ENROLLED BEFORE 2017-2018 EDUCATION SEASON) 2. Basics of Optics & Optical Elements Some about optics Light travels on a strain line path (!) 2. Basics of Optics & Optical Elements Some about optics Light travels on a strain line path (!) Pinhole camera is a good example of this. 2. Basics of Optics & Optical Elements Some about optics Light travels on a strain line path (!) Pinhole camera is a good example of this. 2. Basics of Optics & Optical Elements Some about optics Light travels on a strain line path (!) Speed of light is finite c= 3x108m/s 2. Basics of Optics & Optical Elements Some about optics Light travels on a strain line path (!) Speed of light is finite Refractive index is related with c describes how fast light travels through the material 𝒄 𝒏 λ = 𝒗 λ 2. Basics of Optics & Optical Elements Some about optics Light travels on a strain line path (!) Speed of light is finite Refractive index is related with c Abbe Number; an approximate measure of the material's dispersion (change of refractive index versus wavelength), with high values of abbe number indicating low dispersion nC, nD and nF are the refractive indices of the material at the wavelengths of the Fraunhofer C, D1, and F spectral lines (656.3 nm, 589.3 nm, and 486.1 nm respectively). 2. Basics of Optics & Optical Elements Some about optics Fermat’s Principle and Snell’s Refraction Rule 𝒅 = 𝒗𝒕 𝒄 𝒏= 𝒗 𝒄 𝒅= 𝒕 𝒏 𝒏𝒅 = 𝒄𝒕 ∆ = 𝒏𝒅 ∆ = 𝒏𝟏𝒅𝟏 + 𝒏𝟐𝒅𝟐 + 𝒏𝟑𝒅𝟑 + ⋯ ∆; Optical path length Additive quantity 2. Basics of Optics & Optical Elements Some about optics Fermat’s Principle and Snell’s Refraction Rule If refractive index is not constant in a medium then the time which light travels in that medium is given as; 2. Basics of Optics & Optical Elements Some about optics There are two rules for such process. A portion of the light beam is being reflected as keeping the same angle to the surface normal (Snell’s reflactive law) and a portion of light beam is pass through to the other medium. 2. Basics of Optics & Optical Elements Some about optics There are two rules for such process. Fermat’s Principle: The path taken by a beam between two given points is the path that can be traversed in the least time. According to Fermat’s principle ∆ must be minimum 2. Basics of Optics & Optical Elements Some about optics There are two rules for such process. Fermat’s Principle: The path taken by a beam between two given points is the path that can be traversed in the least time. According to Fermat’s principle ∆ must be minimum 𝒅∆ =𝟎 𝒅𝒙 2. Basics of Optics & Optical Elements Some about optics There are two rules for such process. Fermat’s Principle: The path taken by a beam between two given points is the path that can be traversed in the least time. According to Fermat’s principle ∆ must be minimum 2. Basics of Optics & Optical Elements Some about optics There are two rules for such process. Fermat’s Principle: The path taken by a beam between two given points is the path that can be traversed in the least time. 2. Basics of Optics & Optical Elements Some about optics There are two rules for such process. Fermat’s Principle: The path taken by a beam between two given points is the path that can be traversed in the least time. 2. Basics of Optics & Optical Elements Some about optics There are two rules for such process. Fermat’s Principle: The path taken by a beam between two given points is the path that can be traversed in the least time. 2. Basics of Optics & Optical Elements Some about optics There are two rules for such process. Fermat’s Principle: The path taken by a beam between two given points is the path that can be traversed in the least time. 2. Basics of Optics & Optical Elements Some about optics There are two rules for such process. Fermat’s Principle: The path taken by a beam between two given points is the path that can be traversed in the least time. 2. Basics of Optics & Optical Elements Some about optics There are two rules for such process. Fermat’s Principle: The path taken by a beam between two given points is the path that can be traversed in the least time. ! Snell’s refractive law 2. Basics of Optics & Optical Elements Some about optics Critical Angle: Air Water Critical Angle Inner reflection ! water n1=1.33 Air n2=1 θc=48o.75 2. Basics of Optics & Optical Elements Some about optics The escaped fish is always the big one ! Air Water 2. Optical Elements The coordinate system within which surface locations and ray directions are defined is the standard right-hand Cartesian frame; Illustration of refraction at a spherical surface with an incident ray directed from left to right For a single refracting or reflecting surface the z-axis coincides with the optical axis, with the origin of the coordinate system at the vertex O of the surface. the optical axis is the line of symmetry along which the elements are located. 2. Optical Elements Illustration of refraction at a spherical surface with an incident ray directed from left to right The indices of refraction are n and n' to the left and right of the surface, respectively, with points B, B’ and C on the optical axis of the surface. The line PC is the normal to the interface between the two media at point P, and a ray directed toward B is refracted at P and directed toward B'. The slope angles are u and u’ measured from the optical axis, and the angles of incidence and refraction, respectively, are i and i’ measured from the normal to the surface. The symbols s and s’ denote the object and image distances, respectively, and R represents the radius of curvature of the surface, measured at the vertex. 2. Optical Elements Illustration of refraction at a spherical surface with an incident ray directed from left to right The sign convention for angles is chosen so that all of the angles shown in the figure. Slope angles u and u' are positive when a counterclockwise rotation of the corresponding ray about B or B' brings the ray into coincidence with the z-axis. The angles of incidence and refraction, i and I’ are positive when a clockwise rotation of the corresponding ray about point P brings the ray into coincidence with the line PC. 2.2 PARAXIAL EQUATION FOR REFRACTION Paraxial Approximation: When the point P is close enough to the optical axis so that sines and tangents of angles can be replaced with the angles themselves. In this approximation any ray is close to the axis and nearly parallel to it. From figure Applying the paraxial approximation to distances; s & s’;conjugate points We get; If either s or s' = ∞, then the conjugate distance is the focal length, that is, s = 𝑓 when s’ = ∞ and s’ = 𝑓‘ when s = ∞. 2.2 PARAXIAL EQUATION FOR REFRACTION Power: The right side of the equation contains factors relating to the surface and surrounding media, and not to the object and image. It is useful to denote this combination by P, where P is the power of the surface. Gaussian equation Conjugate points in the paraxial region. B B’, Q Q’ are pairs of conjugates points. 2.2 PARAXIAL EQUATION FOR REFRACTION Magnification: The geometry in Figure can be used to determine the transverse or lateral magnification m, defined as the ratio of image height to object height. In symbols we have m = h'/h, where Because h and h' have opposite signs, the transverse magnification is negative for the case shown. If m < 0, the image is inverted relative to the object; in the case where m > 0 the image is said to be erect. 2.2 PARAXIAL EQUATION FOR REFRACTION In this figure, a ray joining conjugate points B and B' has slope angles u and u'. The angular magnification M is defined as tan(u‘) / tan(u), where from the geometry we see that y = s tan(u) = s’ tan(u’) 2.2 PARAXIAL EQUATION FOR REFRACTION Defining H = nh tan(u), then states that H before refraction is the same as H after refraction. Thus in any optical system containing any number of refracting (or reflecting) surfaces, H is an invariant Lagrange invariant, H is important in at least one other respect; the total flux collected by an optical system from a uniformly radiating source of light is proportional to H2. Its invariance through an optical system is thus a consequence of conservation of energy. 2.3 PARAXIAL EQUATION FOR REFLECTION Applying the sign conventions to the symbols shown gives distances s, s’ and R, and angles i, 𝜙, u, and u’ as negative. The law of reflection is i = -I’ hence the angle of reflection I’ is positive in the figure. From the geometry shown we get 2.3 PARAXIAL EQUATION FOR REFLECTION The law of reflection follows directly from Snell's law of refraction if we make the substitution n' = -n. Remember the power for reflraction P > 0 for a concave mirror and P < 0 for a convex mirror, where a mirror is concave or convex as seen from the direction of the incident light. 2.4 TWO-SURFACE THICK LENS: REFRACTING ELEMENTS 2.4 TWO-SURFACE REFRACTING ELEMENTS THICK LENS: If we assume the lens has index n and is located in air, then n1=n’2=1, and applying Gaussian Eq. to each surface gives; Remember Gaussian equation 2.4 TWO-SURFACE REFRACTING ELEMENTS THICK LENS: If we assume the lens has index n and is located in air, then n1=n’2=1, and applying Gaussian Eq. to each surface gives; Remember Gaussian equation 2.4 TWO-SURFACE REFRACTING ELEMENTS THICK LENS: Both n and d are positive. If the directions of the arrows in Figure are reversed, the foregoing derivation reproduces equation, with P1 and P2 exchanging roles. In this case both d and n change sign and the ratio (d/n) is unchanged in sign. Thus P in Eq. is the same for either direction of light. Note that the effective focal length 𝒇’ in Figure is measured from the intersection of two extended rays, the incident ray to the right and the refracted ray to the left. 2.4 TWO-SURFACE REFRACTING ELEMENTS THIN LENS: A thin lens is defined as one in which the separation of the two surfaces is negligible compared to other axial distances, that is, S2 = s’ effectively. For a thin lens in air, Eq shown with arrow in previous slayt apply directly. Letting s1 = s and s’2 = s’ the addition of these equations gives The net power of a thin lens is simply the reciprocal of its focal length and is the same as that of a thick lens with d = 0 2.4 TWO-SURFACE REFRACTING ELEMENTS THICK PLANE-PARALLEL PLATE: A thick plane-parallel plate, as shown in the Figure below has a zero power but also has an image that is displaced laterally along the optical axis relative to the object. 2.4 TWO-SURFACE REFRACTING ELEMENTS THICK PLANE-PARALLEL PLATE: A thick plane-parallel plate, as shown in Figure below has a zero power but also has an image that is displaced laterally along the optical axis relative to the object. Assuming the plate of index n is in air, n1=n’2=1, n’1=n2=n and noting that s2=s’1-d, we get s1’=ns1, s2’=s1-(d/n). The distance from object to image or 2.4 TWO-SURFACE REFRACTING ELEMENTS THICK PLANE-PARALLEL PLATE: A thick plane-parallel plate, as shown in Figure below has a zero power but also has an image that is displaced laterally along the optical axis relative to the object. Assuming the plate of index n is in air, n1=n’2=1, n’1=n2=n and noting that s2=s’1-d, we get s1’=ns1, s2’=s1-(d/n). The distance from object to image Note that the displacement ∆ is independent of the object distance and, as is true in all cases in the paraxial approximation, independent of height y. or For a typical glass with 𝒏 ≅ 𝟏. 𝟓, we see that ∆ ≅ 𝒅/𝟑. 2.4 TWO-SURFACE REFRACTING ELEMENTS THICK PLANE-PARALLEL PLATE: The distance from object to image Note that the displacement ∆ is independent of the object distance and, as is true in all cases in the paraxial approximation, independent of height y. or For a typical glass with 𝒏 ≅ 𝟏. 𝟓, we see that ∆ ≅ 𝒅/𝟑. In the paraxial approximation an optical system is free of any aberrations, that is, an object point is imaged precisely into an image point. When the exact form of Snell's law is used however, most systems will have some form of aberration. A thick plate is a good example of a simple system with aberration, that is, it fails to take all rays from a single object point into a single image point. This is easily shown by applying Snell's law in its exact form at each surface. With some intermediate steps, the geometry leads to 2.4 TWO-SURFACE REFRACTING ELEMENTS THICK PLANE-PARALLEL PLATE: Paraxial Approx. Exact The image position depends on the ray height at the first surface. 2.5 TWO-MIRROR TELESCOPES Schematic diagrams of Cassegrain Type Telescope 2.5 TWO-MIRROR TELESCOPES Schematic diagrams of Gregorian Type Telescope 2.5 TWO-MIRROR TELESCOPES It is very helpful to describe any two-mirror system in terms of a set of dimensionless or normalized parameters: 2.5 TWO-MIRROR TELESCOPES By using Paraxial Equation for reflection, we can get; The net power of a two-mirror telescope n = 1 for the primary and n = -1 for the secondary, according to the sign convention. 2.5 TWO-MIRROR TELESCOPES The net power of a two-mirror telescope n = 1 for the primary and n = -1 for the secondary, according to the sign convention. For the arrangements shown in Figures, both d and n are negative; the light is traveling from right to left and the secondary mirror is to the left of the primary. Hence d/n is positive. The telescope power is positive for a Cassegrain telescope and negative for a Gregorian. In terms of the focal lengths and focal ratios; 2.5 TWO-MIRROR TELESCOPES For the arrangements shown in Figures, both d and n are negative; the light is traveling from right to left and the secondary mirror is to the left of the primary. Hence d/n is positive. The telescope power is positive for a Cassegrain telescope and negative for a Gregorian. In terms of the focal lengths and focal ratios; 2.5 TWO-MIRROR TELESCOPES Telescope scale: For a telescope of focal length 𝒇 2.5 TWO-MIRROR TELESCOPES Telescope scale: For a telescope of focal length 𝒇 --------------------------------------------------------------------------------------------------------------------1 arcseconds = 1/60 arcminutes = 1/3600 degree. 1 radian = 180/π 1 radian = 60*60*180/π = 206265 arcseconds ÖNEMLİ HATIRLATMA: Bu sunum İ.Ü. İstanbul Fen Fakültesi Lisans öğrencilerinin eğitimlerine ücretsiz katkı sağlamak amaçlı hazırlanmış olup, bilimsel kaynak olarak gösterilemez, ücretlendirilemez, izinsiz kaydedilemez, kullanılamaz, çoğaltılamaz ve ticari bir ürün haline dönüştürülemez. İLGİNİZ ve SABRINIZ İÇİN TEŞEKKÜRLER…