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Chapter 35: Q19P (page 1075)

Suppose that Young鈥檚 experiment is performed with blue-green light of wavelength 500 nm. The slits are 1.20 mm apart, and the viewing screen is 5.40 m from the slits. How far apart are the bright fringes near the center of the interference pattern?

Short Answer

Expert verified

The bright fringes near the center of the interference pattern are apart of 2.25 mm.

Step by step solution

01

Write the given data from the question

Blue-green light Wavelength, $位 = 500 nm$ .

The slit separation, $d = 1.20 mm$ .

The screen distance from the slit, $D = 5.4 m$ .

02

Determine the formulas to calculate how far apart the bright fringes near the center of the interference pattern

The condition for the maxima in Young鈥檚 experiment is given as follows.

$d s i n 胃 = m 位$ 鈥︹€� (1)

Here, d is the distance between the slits, $位$ is the wavelength, mis the order, and $胃$ is the angular separation.

03

Calculate how far apart the bright fringes near the center of the interference pattern

The maximum vertical distance from the center of the pattern is given by,

$\tan 胃鈮� \sin 胃 = \frac{y_{m}}{D}$

Substitute $\frac{y_{m}}{D}$ for $\sin 胃$ into equation (1).

$d (\frac{y_{m}}{D}) = m 位 y_{m} = \frac{m 位 D}{d}$

Substitute 1 for m, 54 m for D, 500 nm for $位$ and $1.20 mm$ for d into above equation.

$y_{m} = \frac{1 脳 500 脳 10^{- 9} 脳 5.4}{1.2 脳 10^{- 3}} = \frac{27 脳 10^{- 7}}{1.2 脳 10^{- 3}} = 22.5 脳 10^{- 4} m = 2.25 mm$ .

Hence the bright fringes near the center of interference pattern are apart of 2.25 mm.

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Most popular questions from this chapter

In the two-slit experiment of Fig.35-10, let angle $胃$ be ${20.0}^{0} C$ , the slit separation be $4.24 渭 m$ , and the wavelength be $位 = 500 nm$ . (a) What multiple of $位$ gives the phase difference between the waves of rays $r_{1}$ and $r_{2}$ when they arrive at point $P$ on the distant screen? (b) What is the phase difference in radians? (c) Determine where in the interference pattern point $P$ lies by giving the maximum or minimum on which it lies, or the maximum and minimum between which it lies?

A double-slit arrangement produces interference fringes for sodium light $(位 = 589 nm)$ that are $0 . 20^{0} C$ apart. What is the angular separation if the arrangement is immersed in water $(n = 1.33)$ ?

A thin film with index of refraction $n = 1.40$ is placed in one arm of a Michelson interferometer, perpendicular to the optical path. If this causes a shift of 7.0 bright fringes of the pattern produced by light of wavelength $589 nm$ , what is the film thickness?

Figure 35-29 shows the transmission of light through a thin film in the air by a perpendicular beam (tilted in the figure for clarity). (a) Did ray $r_{3}$ undergo a phase shift due to reflection? (b) In wavelengths, what is the reflection phase shift for ray $r_{4}$ ? (c) If the film thickness is L, what is the path length difference between rays $r_{3}$ and $r_{4}$ ?

A thin film of acetone $n = 1.25$ coats a thick glass plate $n = 1.50$ White light is incident normal to the film. In the reflections, fully destructive interference occurs at $600 nm$ and fully constructive interference at $700 nm$ . Calculate the thickness of the acetone film.

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