Review To correct near sightedness a corrective lens a diverging lens must form a virtual upright image at the far point dfar in front of the lens of an object located at infinity as shown below Physics for Scientists Engineers 2 1 1 1 d far f To correct far sightedness a corrective lens a converging lens must produce a virtual upright image of the newspaper at the near point dnear of the person s vision as shown below Spring Semester 2005 Lecture 40 1 1 1 0 25 m dnear f March 30 2005 Physics for Scientists Engineers 2 1 March 30 2005 The Telescope Like the microscope telescopes come in many forms First we will discuss the refracting telescope and then we will delve into the reflecting telescope The refracting telescope consists of two lenses In our example we represent the telescope using two thin lenses However an actual refracting telescope will use more sophisticated lenses The objective lens forms a real image of the distance object at distance fo The eyepiece is placed so that the image formed by the objective is a distance fe from the eyepiece The eyepiece forms a virtual magnified image of the image formed by the objective Because the object to be viewed is at a large distance the incoming light rays can be thought of as being parallel The eyepiece forms a virtual image at infinity again producing parallel rays March 30 2005 Physics for Scientists Engineers 2 2 Geometry of the Telescope In the drawing of the geometry of a refracting telescope below the parallel light rays from the object are depicted by a single ray A red black dashed line depicts the parallel light rays forming the virtual image the objective lens and the eyepiece Physics for Scientists Engineers 2 3 March 30 2005 Physics for Scientists Engineers 2 4 Magnification of a Telescope Let s calculate the angular magnification of a refracting telescope The magnification of the telescope is defined as the angle observed in the eyepiece e divided by the angle subtended by the object being viewed o m e f o o fe Because the telescope deals with objects at large distances we cannot calculate the magnification of the telescope using the lens law For example one might try to express the magnification of the objective lens using the lens equation m Calculation of Magnification of Telescope The angle o is the angle subtended by a distant object d o tan o fo The angle e is the apparent angle seen in the eyepiece d e tan e fe The magnification is e d fe fo f m o inverted o d fo fe fe di d i 0 bad do We can get the angular magnification from the geometric drawing on the next slide March 30 2005 Physics for Scientists Engineers 2 5 Example Refracting Telescope fo fe f 19 m fe o 0 076 m 7 6 cm m 250 March 30 2005 Physics for Scientists Engineers 2 6 The objective lens of a refracting telescope is large and heavy The 40 inch refractor at Yerkes weighed 500 pounds Supporting a large glass lens was difficult Must be supported by its edges Constructing the large glass lens was difficult The glass lens was thick and absorbed light m 250 m Physics for Scientists Engineers 2 Problems with Refracting Telescopes The world s largest refracting telescope was completed in 1897 and installed in Williams Bay Wisconsin between Chicago and Milwaukee It had an objective lens of diameter 40 inches 1 0 m with a focal length of 62 feet 19 m What should the focal length of the eyepiece be to give a magnification of 250 fo 19 m March 30 2005 A glass lens has chromatic aberration The 40 inch refracting telescope at Yerkes Observatory Different focal lengths for different colors The solution was to replace the objective lens with a mirror 7 March 30 2005 Physics for Scientists Engineers 2 8 The Reflecting Telescope Basic Reflecting Telescope Most large astronomical telescopes are reflecting telescopes with the objective lens being replaced with a concave mirror Basic reflector Large mirrors are easier to fabricate and position than large lenses The eyepiece is still a lens Various types of reflecting telescopes have been developed We will discuss three examples of the geometries of reflecting telescope Replace the objective lens with a parabolic mirror Reflector This design is impractical because the observer must be in the line of the incident light Newtonian Cassegrain March 30 2005 Physics for Scientists Engineers 2 9 Newtonian Reflecting Telescope The idea for a reflecting telescope came from James Gregory 10 A further improvement on the geometry of the reflecting telescope is the Cassegrain geometry named for the French sculptor Sieur Guillaume Cassegrain first proposed in 1672 Here a small mirror is used to reflect the image through a hole in the center of the objective mirror Newton solved the observer problem by placing a small mirror that reflect the light out to an eyepiece This mirror is small compared with the objective mirror and causes only a small loss of light from the image Physics for Scientists Engineers 2 Physics for Scientists Engineers 2 Cassegrain Geometry for Reflecting Telescope In 1670 Newton presented his design for a reflecting telescope to the Royal Society March 30 2005 March 30 2005 11 This design and many improvements this basic idea are the basis of modern astronomical telescopes March 30 2005 Physics for Scientists Engineers 2 12 The Hubble Space Telescope Hubble Corrected The Hubble Space Telescope HST was deployed April 25 1990 from the Space Shuttle mission STS 31 The original HST objective mirror was produced with a flaw caused by a defective testing instrument The HST orbits the Earth 590 km above the surface of the Earth far above the atmosphere that disturbs the images gathered by ground based telescopes In December 1993 Space Shuttle Service Mission 1 STS 61 deployed the COSTAR package that corrected the flaw in the objective mirror and allowed the HST to begin a spectactular career The two images of the galaxy M100 shown in demonstrate the image quality of the HST before and after the installation of COSTAR The HST is a Ritchey Chr tien reflecting telescope arranged in a Cassegrain geometry This type of telescope uses a concave hyperbolic objective mirror rather than a spherical mirror and a convex hyperbolic secondary mirror This arrangement gives the HST a wide field of view and eliminates spherical aberration The objective mirror is 2 40 m in diameter and has an effective focal length of 57 6 m March 30 2005 Physics for Scientists Engineers 2 13 The James Webb Space Telescope The planned replacement
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