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Chapter 34: Problem 47

A double slit is opposite the center of a 1.8 -m wide screen \(2.0 \mathrm{~m}\) from the slits. The slit separation is \(24 \mu \mathrm{m}\) and the width of each slit is \(7.2 \mu \mathrm{m}\). How many fringes are visible on the screen if the slit is illuminated by \(600 .-\mathrm{nm}\) light?

Short Answer

Expert verified
The width of the screen is 1.8 m. Answer: 36 fringes are visible on the screen.

Step by step solution

01

Calculate the angular separation between bright fringes

We can calculate the angular separation between the bright fringes (maxima) using the double-slit interference formula: \(\theta = \arcsin(\frac{m\lambda}{d})\) Where: - \(\theta\) represents the angular separation between adjacent maxima, - \(m\) represents the order of the maxima, - \(\lambda\) represents the wavelength of the light (600 nm), - and \(d\) represents the slit separation (24 µm). Since we are interested in the angle between adjacent maxima, we will use \(m = 1\): \(\theta = \arcsin(\frac{1 \times 600\,\mathrm{nm}}{24\,\mu\mathrm{m}})\) \(\theta \approx 0.025\) radians
02

Calculate the distance between adjacent fringes on the screen

We can now convert the angular separation to a linear distance on the screen using the following formula: \(y = L \times \tan(\theta)\) Where: - \(y\) represents the distance between adjacent fringes, - \(L\) represents the distance between the slits and the screen (2.0 m), - and \(\theta\) represents the angular separation between adjacent maxima. Substitute the values and calculate \(y\): \(y = 2.0\,\mathrm{m} \times \tan(0.025) \approx 0.05\,\mathrm{m}\)
03

Determine the total number of fringes visible on the screen

To calculate the total number of fringes visible on the screen, we will divide the width of the screen (1.8 m) by the distance between adjacent fringes (\(y\)): Total fringes = \(\frac{1.8\,\mathrm{m}}{0.05\,\mathrm{m}} = 36\) There are 36 fringes visible on the screen.

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Most popular questions from this chapter

A red laser pointer is shined on a diffraction grating, producing a diffraction pattern on a screen behind the diffraction grating. If the red laser pointer is replaced with a green laser pointer, will the green bright spots on the screen be closer together or farther apart than the red bright spots were?

34.35 Monochromatic blue light \((\lambda=449 \mathrm{nm})\) is beamed into a Michelson interferometer. How many fringes move by the screen when the movable mirror is moved a distance \(d=\) \(0.381 \mathrm{~mm} ?\)

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?

Light of wavelength \(653 \mathrm{nm}\) illuminates a slit. If the angle between the first dark fringes on either side of the central maximum is \(32.0^{\circ},\) What is the width of the slit?

White light shines on a sheet of mica that has a uniform thickness of \(1.30 \mu \mathrm{m} .\) When the reflected light is viewed using a spectrometer, it is noted that light with wavelengths of \(433.3 \mathrm{nm}, 487.5 \mathrm{nm}, 557.1 \mathrm{nm}, 650.0 \mathrm{nm}\), and \(780.0 \mathrm{nm}\) is not present in the reflected light. What is the index of refraction of the mica?
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