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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

A diffraction grating having is illuminated with a light signal containing only two wavelengths and . The signal in incident perpendicularly on the grating. (a) What is the angular separation between the second order maxima of these two wavelengths? (b) What is the smallest angle at which two of the resulting maxima are superimposed? (c) What is the highest order for which maxima of both wavelengths are present in the diffraction pattern?

Light of wavelength 600 nm is incident normally on a diffraction grating. Two adjacent maxima occur at angles given by $\sin 胃 = 0.2$ and $\sin 胃 = 0.3$ .The fourth order maxima are missing. (a) What is the separation between adjacent slits? (b) What is the smallest slit width this grating can have? For that slit width , what are the (c) largest, (d) second largest, and (e) third largest values of the order of the maxima produced by the grating?

Figure 36鈥�35 shows the bright fringes that lie within the central diffraction envelope in two double-slit diffraction experiments using the same wavelength of light. Is (a) the slit width $a$ , (b) the slit separation $d$ , and (c) the ratio $d / a$ in experiment B greater than, less than, or the same as those quantities in experiment A?

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?

For the situation in Questions 9 and Fig. 1, if instead we increased the grating spacing, would (a) the half-widths of the lines and (b) the separation of the lines increase, decrease, or remain the same? (c) Would the lines shift to the right, shift to the left, or remain in place?

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