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Chapter 33: Q.63 (page 958)

One day, after pulling down your window shade, you notice that sunlight is passing through a pinhole in the shade and making a small patch of light on the far wall. Having recently studied optics in your physics class, you're not too surprised to see that the patch of light seems to be a circular diffraction pattern. It appears that the central maximum is about 1cmacross, and you estimate that the distance from the window shade to the wall is about 3m.. Estimate (a) the average wavelength of the sunlight (in nm ) and (b) the diameter of the pinhole (in mm ).

Short Answer

Expert verified

a) The average wavelength of the sunlight550nm

b) The diameter of the pinhole0.4mm

Step by step solution

01

Average Wavelength

vaguely remember that when using 位 and aperture diameter D, the expression for the wavelength of the beams emanating from a completely circular probe at position L from the pupil is

w=2.44脳位LD

This means that the beam diameter is linearly proportional to the wavelength used. Therefore, if we want to consider an average wavelength used, assuming the intensity per wavelength was constant, this average will be just the simplest arithmetic mean; in our case, half the sum of the lowermost and uppermost wavelengths of the visible spectrum . That is,

位ovg=位min+位max2=400+7002=550nm

02

Diameter

They can already obtain the aperture's length as

D=2.44脳位Lw

D=2.44脳5.5脳10鈭�7脳3m0.01=4.03脳10鈭�4m=0.4mm(Numerically)

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Most popular questions from this chapter

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