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Chapter 32: Problem 19

Light is incident normally on a grating with 10,000 lines/cm. Find the maximum order in which (a) 450 -nm and (b) 650 -nm light will be visible.

Short Answer

Expert verified
The maximum order in which 450-nm light will be visible is around 2 and 650-nm light will be visible is around 1.

Step by step solution

01

Find the grating spacing

The grating spacing \(d\) is the reciprocal of the number of lines per unit length. The number of lines is given as 10,000 lines/cm, so \(d = \frac{1}{10,000}\) cm.
02

Calculate the maximum order for 450-nm light

Convert the wavelength from nm to cm: \(λ = 450 \times 10^{-7}\) cm. Substitute the derived wavelengths and the calculated grating spacing into the equation for \(n_{max}\): \(n_{max} = \frac{d}{λ} = \frac{1/10,000}{450 \times 10^{-7}}\).
03

Calculate the maximum order for 650-nm light

Convert the wavelength from nm to cm: \(λ = 650 \times 10^{-7}\) cm. Substitute the derived wavelengths and the calculated grating spacing into the equation for \(n_{max}\): \(n_{max} = \frac{d}{λ} = \frac{1/10,000}{650 \times 10^{-7}}\).
04

Round off to get whole numbers

A diffraction order must be a whole number. If the calculated \(n_{max}\) are not whole numbers, they should be rounded down to the nearest whole number, since a fractional order doesn't make physical sense.

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Most popular questions from this chapter

The primary maxima in multiple-slit interference are in the same angular positions as those in double-slit interference. Why, then, do diffraction gratings have thousands of slits instead of just two?

While driving at night, your eyes' irises dilate to 3.1 -mm diameter. If your vision were diffraction limited, what would be the greatest distance at which you could see as distinct the two headlights of an oncoming car, spaced \(1.5 \mathrm{m}\) apart? Take \(\lambda=550 \mathrm{nm}\)

Find the wavelength of light used in a Michelson interferometer if 550 bright fringes go by a fixed point when the mirror moves \(0.150 \mathrm{mm}\)

A double-slit experiment with \(d=0.025 \mathrm{mm}\) and \(L=75 \mathrm{cm}\) uses 550 -nm light. Find the spacing between adjacent bright fringes.

Echelle spectroscopy uses relatively coarse gratings in high order. Compare the resolving power of an 80 -lines/mm echelle grating used in 12 th order with a 600 -lines/mm grating used in first order, assuming the two have the same width.
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