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Chapter 27: Q21PE (page 997)

A diffraction grating has 2000 lines per centimeter. At what angle will the first-order maximum be for 520nm -wavelength green light?

Short Answer

Expert verified

The first order maximum is obtained as 5.970.

Step by step solution

01

Given data

Grating lines on the diffraction grating are 2000 liner per cm, which means that the distance between the two slits isd=1cm20001m100cm=5.0×10-6m

The wavelength of the green light isλ=520nm10-9m1nm=5.20×10-7m

The order of maximum is 1.

02

Evaluating the first-order maximum

In order to calculate the angle, we are supposed to firstly find the distance between slits in the grating, for the value of d, and then solve the equation of the constructive interference,

dsinθ=mλ

The value here is for θwhen m=1.

θ=sin-1λd=sin-15.2×10-7m5.0×10-6m=sin-1(0.104)=5.970

Therefore, the first-order maximum is 5.970.

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Most popular questions from this chapter

The \(300 - m\)-diameter Arecibo radio telescope pictured in Figure \(27.28\) detects radio waves with a \(4.00{\rm{ }}cm\) average wavelength.

(a) What is the angle between two just-resolvable point sources for this telescope?

(b) How close together could these point sources be at the \({\rm{2}}\) million light year distance of the Andromeda galaxy?

Figure \(27.28\) A \(305 - m\)-diameter natural bowl at Arecibo in Puerto Rico is lined with reflective material, making it into a radio telescope. It is the largest curved focusing dish in the world. Although \(D\) for Arecibo is much larger than for the Hubble Telescope, it detects much longer wavelength radiation and its difdfraction limit is significantly poorer than Hubble's. Arecibo is still very useful, because important information is carried by radio waves that is not carried by visible light. (credit: Tatyana Temirbulatova, Flickr)

(a) How wide is a single slit that produces its first minimum for \({\rm{633 - nm}}\)light at an angle of \({\rm{28}}{\rm{.0}}^\circ \)? (b) At what angle will the second minimum be?

Under what conditions can light be modeled like a ray? Like a wave?

Find the angle for the third-order maximum for 580-nm-wavelength yellow light falling on a diffraction grating having 1500 lines per centimeter.

Under what circumstances is the phase of light changed by reflection? Is the phase related to polarization?
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