Download Homework #3 due 2/10

Physics 228
Homework #3 – Due 2/10/17
(Date next to each problem is that of the class when its material will tentatively be covered.)
1) (1/30) You wish to construct a lens with focal length |f | = 25 cm from glass with index of refraction
n = 1.5. What should be the radius of curvatures for each of the following cases:
a) Biconvex lens with equal magnitude radii of curvature on the two sides.
b) Plano-convex lens.
c) Convex-concave diverging lens with R1 = 1.5R2.
2) (2/3) For each of the following lenses, consider an object 2 cm high. For each lens, draw clear and
accurate (to scale) figures showing the object, the three “characteristic” rays (see p. 1107), and the image.
Then compare your measured image distances and image sizes with that you calculate from Eqtns. 36.16
and 36.17. State whether the image is real or virtual in each case.
a) converging lens with focal length f = 4 cm and object distance p = 6 cm.
b) converging lens with focal length f = 5 cm and object distance p = 2.5 cm.
c) diverging lens with focal length f = -5 cm and object distance p = 10 cm.
3) (2/3) a) An object is 30 cm in front of a converging lens with focal length f1 = 20 cm. A second
converging lens, with focal length| f2| = 15 cm is 100 cm behind the first lens. How far behind the first
lens is the final image? Is it real or virtual and is it inverted or right-side-up?
b) Repeat the calculation if the second lens is a diverging lens.
4) (2/6) a) A farsighted woman’s eyes have near points of 100 cm. What should be the focal length of the
contact lenses she uses to correct her vision?
b) A nearsighted man’s eyes have far points of 5 m. What should be the focal length of the contact
lenses he uses to correct his vision?
5) (2/8) The closest star to our solar system is Proxima Centauri, with a diameter of 2.0 x 108 m (about
1/3 that of the sun) and a distance of 9.5 x 1015 m (4.2 light years). The world’s largest optical
telescope is Gran Telescopio Canarios, with an objective mirror with a diameter of 10.4 m and focal
length 16.5 m. The effective focal length of the imaging lens = 11.8 cm. What angle does Proxima
Centauri subtend in the sky and what is the angular size of its image in this telescope? (Give the
angles in radians and in degrees.)
6) (2/8) The overall magnification of a compound microscope is |M|= 300. The distance between the
eyepiece (f = 2.25 cm) and objective lens is 21 cm. What is the focal length of the objective lens and
how far from the lens should the object be placed for the image to be in focus?
What you will need to know for exam (Feb. 15)
1) Law of reflection (Eqtn. 35.2)
2) Meaning of index of refraction (Eqtn. 35.4) and Snell’s Law (Eqtn. 35.8)
3) Meaning of total internal reflection and critical angle (Eqtn. 35.10)
4) Lateral magnification (Eqtn. 36.1)
5) Mirror Equations (Eqtns. 36.5 and 36.6), including appropriate signs.
6) How to draw ray diagrams (with three characteristic rays) for mirrors and lenses (qualitatively only)
7) Lens equations (Eqtns. 36.15 and 36.16), including appropriate signs.
Bring a calculator (but cannot use programs) and ruler (or straight edge).