1. Announcements Exam 2 is scheduled for two weeks from today (April 2) but, due to all the missed days it will be pushed back one week to April 9 Homework: Chapter 6 # 44 & 45 plus Supplemental Problems. Solutions will be posted Monday afternoon.

2. Telescope basics Telescopes either use refraction or reflection to focus light to a point. For refraction, the basic law is Snell’s Law The law of reflection is a much simpler:

3. If the surfaces of a piece of glass are curved, they will focus light to a point The focal length, f, is the distance from the lens axis to the focal point or focal plane. The focal length of a lens depends on the material of the lens and the curvature of the surfaces and is found using the Lens Makers Law Lens Makers Law: R 1 and R 2 are the radii of curvature of the two faces, n is the index of refraction of the glass and d is the center thickness of the lens. If the outside medium is air n outside = 1

4. Sign Convention If the center of curvature is on the opposite side of the surface as the incoming light, R is positive. If the center of curvature is on the same side of the surface as the incoming light, R is negative. A positive focal length is a converging lens and a negative focal length is a diverging lens

5. Examples Determine the focal length of a biconvex lens made of crown glass (n = 1.52) whose surfaces both have a radius of curvature of 25 cm. The lens is 1.50 cm thick at its center. Determine the focal length of a plano-convex lens made of flint glass (n = 1.65). Plano-convex means one side is flat (R = ∞ ) and the other side has a convex shape. The convex side has a radius of curvature of 20 cm and the lens is 1.0 cm thick at the center. Does it make a difference which side of the lens the light is incident on?

6. Example 1 Solution For a biconvex lens R 1 >0 and R 2 <0. For this problem R 1 = +25 cm and R 2 = -25 cm with d = 1.50 cm and n = 1.52

7. Example 2 Solution For a plano-convex lens R 1 = ∞ and R 2 <0. For this problem R 1 = ∞ R 2 = -20 cmd = 1.0 cm and n = 1.65

8. A concave mirror will also focus light to a point For a spherical mirror the focal length is just half the radius of curvature of the mirror. For other shapes the formula is somewhat more complicated Sign Convention f and r are positive for a concave mirror f and r are negative for a convex mirror

9. For any telescope, the most important property is the Light Gathering Power (LGP) d o is the diameter of the objective in mm. This compares the light gathering power of the telescope to that of the human eye (diameter = 7 mm)

10. Examples Compare the light gathering power of the Hubble Space Telescope (2.4 m diameter) to a 10” Newtonian reflector. APSU has a new 20” telescope for the observatory. Compare the light gathering power of the telescope to the human eye (d = 7mm).

11. Example Solutions To compare the light gathering power of two telescopes, take the ratio of the square of their diameters. 1. d Hubble = 2.4 m d 10” = 10” x 2.54 cm / in = 25.4 cm = 0.254 m The Hubble Space Telescope has almost 90 times the light gathering power of a 10” diameter telescope 2. D tele = 20” x 25.4 mm / in = 508 mmd 1 = 7.0 mm

12. The ability of a telescope to resolve fine detail is given by the Rayleigh Criterion is the wavelength of the light being used and d is the diameter of the aperture.  is the smallest resolvable angle of the telescope. Note that this angle is in radians, not degrees

13. Example Using a 10” diameter Newtonian telescope in visible light ( = 500 nm) what is the smallest angular detail that can be resolved? At the distance of the Moon (384,400 km), how large is this in kilometers. The general formula relating arc length (s), angle(  ) and radius (r) is: s = r  How large a telescope would be needed to resolve one of the Apollo lunar landers (~10 meters across) from Earth using visible light ( = 500 nm) ?

14. Example Solution 1. d = 10” x 0.0254 m / in = 0.254 m = 500 x 10 -9 m r Moon = 384,400 km using s = r  where r = r Moon To see the lunar lander first find the angle  then find d