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Chapter 27: Q30PE (page 997)

What is the spacing between structures in a feather that acts as a reflection grating, given that they produce a first-order maximum for 525鈥�nmlight at a 30.0掳angle?

Short Answer

Expert verified

The spacing between the structures in a feather is1.05脳10鈥�6m.

Step by step solution

01

Given data

The wavelength of the light is位=525nm10鈥�9m1nm=5.25脳10鈥�7鈥�m

The order of maximum is 1.

The angle at which the first-order maximum is observed 30.0掳

02

Evaluating the spacing between the structures

The equation of the constructive interference can be expressed as

胃蝉颈苍位 鈥︹赌︹赌︹赌︹赌︹赌︹赌�(1)

Where, d,位, 胃and m is the separation between slits, the wavelength of the incident light, and the angle made with the maximum and order of maximum, respectively.

Therefore, if we substitute the given data in equation (1) for m=2, we will get,

localid="1654246211111" d=m位蝉颈苍胃=1脳5.25脳10鈥�7msin30.0掳=1.05脳10鈥�6m

Therefore, the spacing between the structures is 1.05脳10鈥�6nm.

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Most popular questions from this chapter

If a beam of white light passes through a diffraction grating with vertical lines, the light is dispersed into rainbow colors on the right and left. If a glass prism disperses white light to the right into a rainbow, how does the sequence of color compare with that produced on the right by a diffraction grating?

(a) What is the minimum width of a single slit (in multiples of 位 ) that will produce the first minimum for a wavelength 位 ? (b) What is its minimum width if it produces 50 minima? (c) 1000 minima?

When particles scattering light are much smaller than its wavelength, the amount of scattering is proportional to1/位4. Does this mean there is more scattering for small 位 than large 位? How does this relate to the fact that the sky is blue?

A non-reflective coating like the one described in Example 27.6 works ideally for a single wavelength and for perpendicular incidence. What happens for other wavelengths and other incident directions? Be specific.

How do wave effects depend on the size of the object with which the wave interacts? For example, why does sound bend around the corner of a building while light does not?
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