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Chapter 36: Q9P (page 1109)

Aslit $1.00 mm$ wide is illuminated by light of wavelength $589 nm$ . We see a diffraction pattern on a screen $3.00 m$ away. What is the distance between the first two diffraction minima on the same side of the central diffraction maximum?

Short Answer

Expert verified

The distance between first two diffraction minima is $1.77 mm$ .

Step by step solution

01

Identification of given data

The wavelength of the light wave is $位 = 589 nm$

The distance of screen from slit is $D = 3 m$ .

The width of slit is $d = 1 mm$ .

The order of first minima is $m_{1} = 1$ .

The order of second minima is $m_{2} = 2$ .

02

Concept used

The distance between two successive diffraction minima is called the fringe width. It varies with the wavelength, slit width and distance of screen from slit.

03

Determination of distance between first two diffraction minima

The distance between first two diffraction minima is given as:

$w = \frac{(m_{2} - m_{1}) 位 D}{d}$

Substitute all the values in equation.

$w = \frac{(2 - 1) (589 nm) (\frac{10^{- 9} m}{1 nm}) (3 m)}{(1 mm) (\frac{10^{- 3} m}{1 mm})} = 1.77 脳 10^{- 3} m = (1.77 脳 10^{- 3} m) (\frac{1 mm}{10^{- 3} m}) = 1.77 mm$

Therefore, the distance between first two diffraction minima is $1.77 mm$ .

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Most popular questions from this chapter

In the single-slit diffraction experiment of $F i g . 36 - 4$ ,let the wavelength of the light be $500 nm$ , the slit width be localid="1664272054434" $6 渭尘$ , and the viewing screen be at distance localid="1664272062951" $D = 3.00 m$ . Let y axis extend upward along the viewing screen, with its origin at the center of the diffraction pattern. Also let $I_{p}$ represent the intensity of the diffracted light at point P at $y = 15.0 cm$ . (a) What is the ratio of $I_{p}$ to the intensity $I_{m}$ at the center of the pattern? (b) Determine where point P is in the diffraction pattern by giving the maximum and minimum between which it lies, or the two minima between which it lies.

What must be the ratio of the slit width to the wavelength for a single slit to have the first diffraction minimum at $胃 = 45 掳$ ?

A spy satellite orbiting at 160 km above Earth鈥檚 surface has a lens with a focal length of 3.6 m and can resolve objects on the ground as small as 30 cm. For example, it can easily measure the size of an aircraft鈥檚 air intake port. What is the effective diameter of the lens as determined by diffraction consideration alone? Assume $位 = 550 nm$ .

In a single-slit diffraction experiment, the top and bottom rays through the slit arrive at a certain point on the viewing screen with a path length difference of 4.0 wavelengths. In a phasor representation like those in Fig 36-7, how many overlapping circles does the chain of phasors make?

X rays of wavelength $0.12 鈥� nm$ are found to undergo second order reflection at a Bragg angle of $28 掳$ from a lithium fluoride crystal. What is the interplanar spacing of the reflecting planes in the crystal?

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