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Chapter 33: Q. 13 (page 955)

The two most prominent wavelengths in the light emitted by a hydrogen discharge lamp are $656 nm$ (red) and $486 nm$ (blue). Light from a hydrogen lamp illuminates a diffraction grating with $500 lines / mm$ , and the light is observed on a screen $1.50 m$ behind the grating. What is the distance between the first-order red and blue fringes?

Short Answer

Expert verified

The distance between red and blue fringes is $14.5 cm$ .

Step by step solution

01

Formula for distance

The center of the $m$ -th fringe is given by,

$Y_{m} = {尝迟补苍胃}_{m}$

$= Ltan (\sin^{- 1} (\frac{尘位}{d}))$

localid="1649218383524" $d$ is the distance between gratings

localid="1649218434130" $位$ is wavelength

localid="1649218442071" $胃_{m}$ is diffraction angle

02

Calculation for distance

The grating constant is $500 lines / mm$ .

There will be a space between two succeeding gratings.

$d = \frac{1 脳 10^{- 3}}{500}$

$= \underset{炉}{2 脳 10^{- 6} m}$

So,

$螖驰 = {尝迟补苍胃}_{1, red} - {尝迟补苍胃}_{1, blue}$

$= L [\tan (\sin^{- 1} (\frac{位_{red}}{d})) - \tan (\sin^{- 1} (\frac{位_{blue}}{d}))]$

In terms of numbers,

$螖驰 = 1.5 [\tan (\sin^{- 1} (\frac{0.656}{2})) - \tan (\sin^{- 1} (\frac{0.486}{2}))]$

$= 14.5 cm$

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Most popular questions from this chapter

FIGURE shows the light intensity on a screen $2.5 m$ behind an aperture. The aperture is illuminated with light of wavelength $620 n m$ .

a. Is the aperture a single slit or a double slit? Explain.

b. If the aperture is a single slit, what is its width? If it is a double slit, what is the spacing between the slits?

A radar for tracking aircraft broadcasts a $12 GHz$ microwave beam from a $2.0 鈭� m$ -diameter circular radar antenna. From a wave perspective, the antenna is a circular aperture through which the microwaves diffract.

a. What is the diameter of the radar beam at a distance of $30 km$ ?

b. If the antenna emits $100 kW$ of power, what is the average microwave intensity at $30 km$ ?

A double-slit experiment is set up using a helium-neon laser $(位 = 633 nm)$ . Then a very thin piece of glass $(n = 1.50)$ is placed over one of the slits. Afterward, the central point on the screen is occupied by what had been the $m = 10$ dark fringe. How thick is the glass?

A Michelson interferometer operating at a $600 n m$ wavelength has a $2.00 - c m$ -long glass cell in one arm. To begin, the air is pumped out of the cell and mirror $M 2$ is adjusted to produce a bright spot at the center of the interference pattern. Then a valve is opened and air is slowly admitted into the cell. The index of refraction of air at $1.00 a t m$ pressure is $1.00028$ . How many brightdark-bright fringe shifts are observed as the cell fills with air?

Light of $630 nm$ wavelength illuminates a single slit of width $0.15 mm$ . FIGURE $EX 33.17$ shows the intensity pattern seen on a screen behind the slit. What is the distance to the screen $?$

See all solutions

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