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Chapter 33: Q. 39 (page 956)

A diffraction grating having 500lines/mmdiffracts visible light at 30∘.What is the light's wavelength?

Short Answer

Expert verified

The wavelength of sunshine is λ=500nm.

Step by step solution

01

Step: 1 Finding the grating spacing:

The constant value of grating is 500lines/mm,the spacing by

d=1mm500d=2×10−6m.

02

Step: 2 Equating the equation:

In equation of grating,the light diffraction light wavelength by

dsin⁡θm=mλ⇒λ=dsin⁡θmm.

03

Step: 3 Obtaining the wavelength value:

From expression of wavelength

λ=2×10−6×sin⁡30∘mλ=1000nmm.

As we're seeing, there should only be one value of mthat corresponds to a wavelength within the visible region and therfore the mwill be 2,The wavelength are500nm.

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Most popular questions from this chapter

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 ).

FIGURE P33.56 shows the light intensity on a screen behind a single slit. The wavelength of the light is 600nmand the slit width is 0.15mm. What is the distance from the slit to the screen?

Scientists shine a laser beam on a 35−μm-wide slit and produce a diffraction pattern on a screen 70cmbehind the slit. Careful measurements show that the intensity first falls to 25% of maximum at a distance of 7.2mm from the center of the diffraction pattern. What is the wavelength of the laser light?

Scientists use laser range-finding to measure the distance to the moon with great accuracy. A brief laser pulse is fired at the moon, then the time interval is measured until the "echo" is seen by a telescope. A laser beam spreads out as it travels because it diffracts through a circular exit as it leaves the laser. In order for the reflected light to be bright enough to detect, the laser spot on the moon must be no more than 1.0kmin diameter. Staying within this diameter is accomplished by using a special large diameter laser. If λ=532nm, what is the minimum diameter of the circular opening from which the laser beam emerges? The earth-moon distance is384,000km.

In a single-slit experiment, the slit width is 200 times the wavelength of the light. What is the width (inmm)of the central maximum on a screen 2.0m behind the slit?
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