# astronomical telescope magnification formula

The Hour Angle is negative east of and positive west of the meridian (as right ascension increases eastward). Gamma (Pherkad) ……………….. 3.1 The separation between the objective and an eye piece is 36 cm and the final image is formed at infinity. Look at the image of Saturn on this page. If we wanted more magnification, we could use an eyepiece with a shorter focal length, such as 10mm: 1200mm/10mm = 120x magnification We could also use these eyepieces with a … The diameter of the first image equals the film diagonal (44 mm for 35 mm film) divided by the magnification. Fe is the focal length of the ocular (divided by Barlow F is the focal length of the objective Formula: 2.5 X Telescope Aperture (Maximum: 350x) M is the magnification, (the second formula is based on Lambda = 0.00055 for yellow) where r is the angular radius (one-half the angular diameter) of the Airy disc (irreducible min. Under ideal conditions, the human eye can resolve anything subtending more than a 1′ angle, i.e., see an object as an extended object or see a double star as two stars rather than a single point of light, provided that the two components are of nearly equal brightness. As FIG. 0.8*D Focal Length is how far light travels inside the telescope before it reaches a focus point. Delta (Megrez) ……………….. 3.4 Fc/Fe is the projection magnification Sun, Moon …………………………………………. Maximum Telescope Magnification Calculator Calculate the theoretical maximum magnification possible with a particular telescope. Normal high power, double stars …………….. 1.2*D to 1.6*D The slop is derived from the formula Theta = k*(h/F), Magnification depends on the focal length of the telescope and the focal length of the eyepiece. Epsilon ………………………………. k is a constant with a value of 57.3 for Theta in degrees, 3438 in Maximum useful magnification ……………….. 2.0*D F’ is the effective focal length of the system The first formula yields image size of the sun and moon as approximately 1% of the effective focal length (Since visual magnification is the ratio of the objective to ocular focal length, the combination of prime-focus camera and off-axis guider with a 12.5-mm ocular gives a guiding magnification of f/12.5. practically 8-25′, 1-2′ for good eyes. d = f/f-number (by substituting F/f for M) (The Moon is approximately 400 times smaller in angular diameter than the Sun, but is approximately 400 times closer.) Thus, a 2-minute exposure at f/1.4 is equivalent to a 32-minute exposure at f/5.6 (4 stops squared times 2 minutes), ignoring the effects of reciprocity failure in the film, which would mean that the 32-minute exposure would have to be even longer. Alpha Ursae Majoris (Dubhe) to Beta Ursae Majoris (Merak) . The formula for Exit Pupil Diameter: Sample Computation: For instance, you have a telescope with an aperture focal length of 100 mm, eyepiece focal length 10 mm, scope focal length 500 mm, and magnification power of 50x. Alpha is the apparent field Too much magnification can be as unsatisfactory as too little. Print Enlargement is the amount of enlargement of the print (3x is the standard for 35-mm film), h = (Theta*F)/k To compare the relative light grasp of two main lenses used at the same magnification, compare the squares of their diameters. Best visual acuity …………………………………. F is the focal length of the objective f is the focal length of the ocular At prime focus (ground glass), magnification is 1x for each 25 mm of F MAGNIFICATION: BY DIAMETER AND EXIT PUPIL F is the focal length of the objective Delta (Pherkard) …………………. 2.3 The total angular magnification when accommodation of eye is maximum. matches resolution of telescope) …………… 0.5*D M is the projection magnification, equal to (B/Fe)-1 57.3 is the number of degrees in a radian F is the effective focal length (focal length times Barlow magnification) in mm Guidescope EFL is the guidescope’s effective focal length, the guidescope’s focal length times any Barlow magnification (should be >= to the focal length of the primary and the guidescope’s magnification, 0.2x per mm of focal length of the objective, 0.1x per mm of the camera lens. f is the f-number (f/) of the objective, where Theta is the smallest resolvable angle in ” M = D/6 = 17*D (by substituting 6 mm for d and taking the reciprocal), where M is the minimum magnification without wasting light Use 20x for a clock drive. Width of Orion’s belt ………………………………. 11.23 - Be able to use the formula for the magnification of a telescope: fo = magnification. where d is the exit pupil f/7.5 (as with a typical focal reducer that reduces the effective focal length by a factor of 0.6) is a significant improvement. Maximum Resolution is the max resolution for a perfect lens k is a constant with a value of 57.3 for Theta in degrees, 3438 in minutes of arc, 206265 for seconds of arc (the number of the respective units in a radian). (Since visual magnification is the ratio of the objective to ocular focal length, the combination of prime-focus camera and off-axis guider with a 12.5-mm ocular gives a guiding magnification of f/12.5. (Theta/k = 0.5/57.3 = 0.009). 0.25*D B is the secondary image (“throw”), the distance of the ocular center from the focal plane of the film, Resolution = (2*Dawes Limit*3476)/1800) = Dawes Limit * 38.8, where Resolution is the smallest resolvable lunar feature in km Fe is the focal length of the ocular, where f/ is the f-number of the system Beta (Merak) ………………….. 2.4 Theta is the object’s angular height (angle of view) in units corresponding to k M/D is the power per mm. 13° /h (1.08°/5 min) at 30° declination Thus: TELESCOPE FOCAL LENGTH / OCULAR FOCAL LENGTH = MAGNIFICATION where Length is the length in mm of the star trail on film minutes of arc, 206265 for seconds of arc (the number of the respective units in a radian). Compute for the exit pupil diameter of the scope. d is the diameter of the exit pupil There are several important factors to consider with telescope magnification: magnification, true field, apparent field, exit pupil, and resolution. F is the focal length of the objective 18° A is the distance of the Barlow center from the focal point of the telescope objective D is the diameter of the objective center of the other). B/A is the projection magnification (Barlow mag. Example: the 24 mm height, 36 mm width, and 43 mm diagonal of 35-mm film yields an angle of view of 27 deg, 41 deg, and 49 deg