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Unformatted text preview: P202 Spring 2006
Ch 26: Geometrical Optics Homework due at 11:59pm March 19, 2006
Error allowance on all numerical answers is 3% l. A ray of light reﬂects from a plane mirror with an angle of incidence of [30 —— 50] degrees. If the mirror is rotated by an angle 0 = [10.0 —— 15.0] degrees, through
what angle is the reﬂected ray rotated? Solution: 20 2. Is the image formed by reﬂection from all three mirrors of a three—dimensional
corner reﬂector upright [radio button] or inverted [radio button]? 13 the image
inverted left to right? [choice of yes or no] The easiest way to think about this is to imagine the 3 mirrors being two walls
and the ﬂoor at the corner ofa room. The image formed by each of the “walls”
individually is left—right inverted but upright. Thus the image formed by reﬂection
from the two walls is not LR inverted ( the second L—R inversion undoes the first
one) and upright. Finally, the “floor” creates an image of the image created by
the two “walls This does not change the LR inversion but does make an image
that is upside down. Perhaps a better way to think of the problem is to draw three Cartesian axes
{x,y,z) as the object with each axis being parallel to the intersection ofa pair of
the corner reflector’s three mirrors. The image that involves reﬂection in all of
the three mirrors has each of the Cartesian axes inverted with respect to the object. Thus, whatever direction you call “up" in the object is reversed in the
image. Solutions: inverted; no 3. The virtual image produced by a convex mirror is one quarter the size of the object.
(a) If the object is d : [30 — 40] cm in front of the mirror, what is the image
distance? cm
(b) What is the radius of curvature of the mirror? cm Since the image is virtual, di is negative. Solutions: (a) ~d/4 ; (b) 2d/3 4. A submerged scuba diver looks up toward the calm surface of a freshwater lake and notes that the sun appears to be 6 = [30 — 40] degrees from the vertical. The
diver’s friend is standing on the shore at the edge of the lake. At what angle above the horizon does the friend see the sun? degrees
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‘9‘, 41»le aimm L.W~W = a“ " EH be ’ : ‘io su."(1.3zs...9) Solution: 90 — sin’](l.33 sin 6) [note that sin’l must be evaluated in degrees] 5. A small insect v1ewed through a convex lens  1 ~ . 1 . [d = 1.0—
1.5] cm from the lens and appears twice its actual size and inverted.
(a) What is the focal length of the lens assuming it is made of glass? cm
(b) What is the focal length required to achieve the same result if a
polycarbonate lens is used? cm J— + is .1. ms‘éi Swat; who»? do twunﬁd (44'3“: +V¢L f a...
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’25:: m. matm» M 11;... 5mg cm ta.) Solutions (a) 2 d/3 ; (b) ;2d/3 6. Makeup l shaving mirrors usually have one flat side and one concave side. You
find that you can project a magnified image of a light bulb onto the wall of your
bathroom if you hold the mirror [u =1.0 — 1.5] m from the bulb and [v = 3.0 3.5]
m from the wall. (a) What is the magnification of the image?
(b) Is the image erect [radio button] or inverted [radio button]?
(c) What is the focal length of the mirror? m (Ox) mg; —U/UL .—. L113” 7,.st “U“ + .L
11" mu” T .L2i
Lalf u Solutions: (a) — v/u; (b) inverted; (c) u v / (u + v) 7. A friend tells you that when he holds his eyeglasses [d = 20 — 25] cm above a
printed page the print appears the same way up but reduced to [m = 0.60 — 0.70]
of its actual size. (a) Is the image of the print real [radio button] or virtual [radio button]?
(b) What is the focal length of your friend’s glasses? cm
(C) Is you friend nearsighted [radio button] or farsighted [radio button]? (a) Upright images produced by either a convex or a concave lens are always virtual. {bl 4—... J... = J. :12. i = M"! _ a Mal
d mcl f .5: Mal 9 4 (10'1“ I)
CC) ’3ch \M<l 4m vVe. 6a It]. leMr M meats... Cumming, lEME 0cm uueal t5 com..et «A9114, 5%}: Solutions: (a) virtual; (b) rn d l (m — l); (c) nearsighted 8. A 45° — 90°  45° prism is placed on a flat table with one side vertical. A
horizontal beam of light enters the prism through its inclined face and exits through the vertical face at an angle of [8 = 30 — 40] degrees to the horizontal.
What is the refractive index of the prism? 93:45"82
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light incident on the ﬂat end of the fiber cut at 90° to the fiber axis? 3W8.— 'Y\QW‘SL (3 W1. 39, {a {1) (mi) why m “C: '19.}! 6‘ Jim " “l I
{31‘ L ”wt [HR '1 i k. “ I” (z. 7.? E {HQ ‘E‘wt 1:131. *5 “~21
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”Tl/WJ WA. 112%“... i 4? Jun “2. 5 /V1 2» I/n 1 e. it _~ l “r" i r: n P l I ta, “n > E.
Solution: 1.414 10. The focal length of a lens is inversely proportional to (n — 1) where n is the
refractive index of the lens material. The value of n depends on the color of light
passing through the lens. For flint glass, the index of refraction is 1.572 for red
light and L605 for violet light. Suppose a white object is placed [u = 20 — 25] cm
from a ﬂint—glass lens. If the red light reﬂected from the object forms a sharp image [v = 50 — 60] cm from the lens, at what distance from the lens will the
violet image be found? Solution: u v I (1.058 u + 0.058 v) 41v 6:2 I
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 Spring '09
 WARREN
 Physics

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