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Chapter 36: Q19P (page 1110)

How far from grains of red sand must you be to position yourself just at the limit of resolving the grains if your pupil diameter is 1.5mm, the grains are spherical with radius50渭m , and the light from the grains has wavelength 650nm? (a) If the grains were blue and the light from them had wavelength 400nm, would the answer to (b) be larger or smaller?

Short Answer

Expert verified
  1. The distance between the grains and the eye is19.0cm .
  2. Length L will be larger

Step by step solution

01

Introduction

Wavelength is the distance between identical points (adjacent crests) in the adjacent cycles of a waveform signal propagated in space or along a wire.

02

Calculation

The pupil鈥檚 diameter'd'=1.55mm

The radius of sphereR=50鈥�渭m and wavelength '位'=650mm

Since 胃R=1.22位d=胃i

d=1.22脳650脳10-9m1.5脳10-3m胃R=5.286脳10-4鈥�rad

Diameter of the sphere is

D=2R=250渭m=100渭m

03

(a) Determine the distance between grains and the eye

The distance between the grains and the eye is

\begingatheredL=Dd1.22位=D胃R=100脳10-4m5.2867脳10-4rad=18.9cmL=19.0cm

Hence, the distance is 19.0cm.

04

(b) Determine the wavelength is larger & smaller

If wavelength 位=400mm

Since L=Dd1.22位

L伪1位

Since 位=400nm is smaller than 650nm,

Hence, length L will be larger larger.

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Most popular questions from this chapter

A double-slit system with individual slit widths of 0.030鈥尘尘and a slit separation of localid="1663157041233" 0.18鈥尘尘 is illuminated with localid="1664276472239" 500鈥塶尘light directed perpendicular to the plane of the slits. What is the total number of complete bright fringes appearing between the two first-order minima of the diffraction pattern? (Do not count the fringes that coincide with the minima of the diffraction pattern.)

A circular obstacle produces the same diffraction pattern as a circular hole of the same diameter (except very near u 0).Airborne water drops are examples of such obstacles. When you see the Moon through suspended water drops, such as in a fog, you intercept the diffraction pattern from many drops. The composite of the central diffraction maxima of those drops forms a white region that surrounds the Moon and may obscure it. Figure 36-43 is a photograph in which the Moon is obscured. There are two faint, colored rings around the Moon (the larger one may be too faint to be seen in your copy of the photograph). The smaller ring is on the outer edge of the central maxima from the drops; the somewhat larger ring is on the outer edge of the smallest of the secondary maxima from the drops (see Fig. 36-10).The color is visible because the rings are adjacent to the diffraction minima (dark rings) in the patterns. (Colors in other parts of the pattern overlap too much to be visible.) (a) What is the color of these rings on the outer edges of the diffraction maxima? (b) The colored ring around the central maxima in Fig. 36-43 has an angular diameter that is 1.35 times the angular diameter of the Moon, which is 0.50掳. Assume that the drops all have about the same diameter. Approximately what is that diameter?

Light of wavelength 600 nm is incident normally on a diffraction grating. Two adjacent maxima occur at angles given by sin胃=0.2andsin胃=0.3 .The fourth order maxima are missing. (a) What is the separation between adjacent slits? (b) What is the smallest slit width this grating can have? For that slit width , what are the (c) largest, (d) second largest, and (e) third largest values of the order of the maxima produced by the grating?

A diffraction grating has resolving power R=位avg螖位=Nm. (a) Show that the corresponding frequency range f that can just be resolved is given by 鈭�f=c狈尘位. (b) From Fig. 36-22, show that the times required for light to travel along the ray at the bottom of the figure and the ray at the top differ by 鈭�t=(NdC)sin胃. (c) Show that (螖蹿)(螖迟), this relation being independent of the various grating parameters. Assume N鈮�1.

At night many people see rings (called entoptic halos) surrounding bright outdoor lamps in otherwise dark surroundings. The rings are the first of the side maxima in diffraction patterns produced by structures that are thought to be within the cornea (or possible the lens) of the observer鈥檚 eye. (The central maxima of such patterns overlap the lamp.) (a) Would a particular ring become smaller or larger if the lamp were switched from blue to red light? (b) If a lamp emits white light, is blue or red on the outside edge of the ring?
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