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Nostrana [21]
3 years ago
8

A double-slit diffraction pattern is formed on a distant screen. If the separation between the slits decreases, what happens to

the distance between interference fringes? Assume the angles involved remain small.The distance between interference fringes remains the same.The effect cannot be determined unless the distance between the slits and the screen is known.The distance between interference fringes also decreases.The distance between interference fringes increases.
Physics
1 answer:
LenKa [72]3 years ago
7 0

Answer:

The distance between interference fringes increases.

Explanation:

In a double-slit diffraction pattern, the angular position of the nth-maximum in the diffraction patter (measured with respect to the central maximum) is given by

sin \theta = \frac{n \lambda}{d}

where

\theta is the angular position

\lambda is the wavelength

d is the separation between the slits

In this problem, the separation between the slits decreases: this means that d in the formula decreases. As we see, the value of sin \theta (and so, also \theta) is inversely proportional to d: so, if the d decreases, then the angular separation between the fringes increases.

So, the correct answer is

The distance between interference fringes increases.

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A spy camera is said to be able to read the numbers on a car's license plate. If the numbers on the plate are 4.30 cm apart, and
Maslowich

Answer:

D = 2.38 m

Explanation:

This exercise is a diffraction problem where we must be able to separate the license plate numbers, so we must use a criterion to know when two light sources are separated, let's use the Rayleigh criterion, according to this criterion two light sources are separated if The maximum diffraction of a point coincides with the first minimum of the second point, so we can use the diffraction equation for a slit

         a sin θ  = m λ

Where the first minimum occurs for m = 1, as in these experiments the angle is very small, we can approximate the sine to the angle

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Also when we use a circular aperture instead of slits, we must use polar coordinates, which introduce a numerical constant

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Let's apply this equation to our case

         D = 1.22 λ /  θ

To calculate the angles let's use trigonometry

         tan  θ = y / x

          θ = tan⁻¹  y / x

          θ = tan⁻¹ (4.30 10⁻² / 140 10³)

          θ = tan⁻¹ (3.07 10⁻⁷)

          θ = 3.07 10⁻⁷ rad

Let's calculate

        D = 1.22 600 10⁻⁹ / 3.07 10⁻⁷

        D = 2.38 m

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