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Chapter 34: Problem 24

For a double-slit experiment, two 1.50 -mm wide slits are separated by a distance of \(1.00 \mathrm{~mm} .\) The slits are illuminated by a laser beam with wavelength \(633 \mathrm{nm} .\) If a screen is placed \(5.00 \mathrm{~m}\) away from the slits, determine the separation of the bright fringes on the screen.

Short Answer

Expert verified
Answer: The separation between the bright fringes on the screen is 3.165 mm.

Step by step solution

01

Gather given information

In this problem, we are given the following information: - The width of each slit is \(1.50 \ \mathrm{mm}\) - The distance between the two slits is \(1.00 \ \mathrm{mm}\) - The wavelength of the laser beam is \(633 \ \mathrm{nm}\) - The distance between the screen and slits is \(5.00 \ \mathrm{m}\)
02

Convert units to meters

Before proceeding, we need to make sure all units are in meters for consistency. We will convert the given values to meters: Width of each slit = \(1.50 \ \mathrm{mm} = 1.50 \times 10^{-3} \ \mathrm{m}\) Distance between the slits = \(1.00 \ \mathrm{mm} = 1.00 \times 10^{-3} \ \mathrm{m}\) Wavelength of the laser beam = \(633 \ \mathrm{nm} = 633 \times 10^{-9} \ \mathrm{m}\)
03

Recall the formula for the location of bright fringes

In a double-slit experiment, the formula for the location of bright fringes on the screen is given by: \(y = \frac{m \lambda D}{d}\), where \(m\) is the order number of the bright fringe (integer value), \(\lambda\) is the wavelength of the light, \(D\) is the distance between the screen and the slits, and \(d\) is the distance between the two slits.
04

Calculate the separation between consecutive bright fringes

To find the separation of the bright fringes on the screen, we'll find the difference in position between two consecutive bright fringes (i.e., the difference between \(y\) values for \(m\) and \(m+1\)): \(\Delta y = y_{m+1} - y_m = \frac{(m+1) \lambda D}{d} - \frac{m \lambda D}{d}\) This simplifies to: \(\Delta y = \frac{\lambda D}{d}\) Now, substitute the given values and calculate the separation between the consecutive bright fringes: \(\Delta y = \frac{633 \times 10^{-9} \ \mathrm{m} \times 5.00 \ \mathrm{m}}{1.00 \times 10^{-3} \ \mathrm{m}}\) \(\Delta y = 3.165 \times 10^{-3} \ \mathrm{m}\)
05

Convert the result to millimeters

Finally, convert the result to millimeters for a more convenient unit: \(\Delta y = 3.165 \times 10^{-3} \ \mathrm{m} \times \frac{1000 \ \mathrm{mm}}{1 \ \mathrm{m}} = 3.165 \ \mathrm{mm}\) The separation between the bright fringes on the screen is \(3.165 \ \mathrm{mm}\).

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Most popular questions from this chapter

Plane light waves are incident on a single slit of width \(2.00 \mathrm{~cm} .\) The second dark fringe is observed at \(43.0^{\circ}\) from the central axis. What is the wavelength of the light?

Think of the pupil of your eye as a circular aperture \(5.00 \mathrm{~mm}\) in diameter. Assume you are viewing light of wavelength \(550 \mathrm{nm}\), to which your eyes are maximally sensitive. a) What is the minimum angular separation at which you can distinguish two stars? b) What is the maximum distance at which you can distinguish the two headlights of a car mounted \(1.50 \mathrm{~m}\) apart?

Which of the following light types on a grating with 1000 rulings with a spacing of \(2.00 \mu \mathrm{m}\) would produce the largest number of maxima on a screen \(5.00 \mathrm{~m}\) away? a) blue light of wavelength \(450 \mathrm{nm}\) b) green light of wavelength \(550 \mathrm{nm}\) c) yellow light of wavelength \(575 \mathrm{nm}\) d) red light of wavelength \(625 \mathrm{nm}\) e) need more information

Coherent monochromatic light passes through parallel slits and then onto a screen that is at a distance \(L=2.40 \mathrm{~m}\) from the slits. The narrow slits are a distance \(d=2.00 \cdot 10^{-5} \mathrm{~m}\) apart. If the minimum spacing between bright spots is \(y=6.00 \mathrm{~cm},\) find the wavelength of the light.

In a double-slit experiment, He-Ne laser light of wavelength \(633 \mathrm{nm}\) produced an interference pattern on a screen placed at some distance from the slits. When one of the slits was covered with a thin glass slide of thickness \(12.0 \mu \mathrm{m},\) the central fringe shifted to the point occupied earlier by the 10 th dark fringe (see figure). What is the refractive index of the glass slide? (a) Without the glass slide (b) With glass slide
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