Ch 35: Interference

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경

Young & Freedman Calc 14th Edition

Ch 35: Interference

문제 20a

35장, 문제 20a

Two slits spaced 0.260 mm apart are 0.900 m from a screen and illuminated by coherent light of wavelength 660 nm. The intensity at the center of the central maximum (u = 0°) is I₀. What is the distance on the screen from the center of the central maximum to the first minimum

검증된 단계별 안내

Step 1: Recognize that this is a double-slit interference problem. The first minimum occurs where the path difference between the light from the two slits is equal to half a wavelength (λ/2). This condition corresponds to destructive interference.

Step 2: Use the formula for the position of minima in a double-slit interference pattern:

y = \frac{m}{d} \cdot \frac{λ}{L}

, where

y

is the distance from the central maximum to the minimum on the screen,

m

is the order of the minimum (for the first minimum,

m = 1

d

is the slit separation,

λ

is the wavelength of the light, and

L

is the distance from the slits to the screen.

Step 3: Substitute the given values into the formula. Here,

d = 0.260 mm = 0.260 x 10 ⁻ 3 m

λ = 660 nm = 660 x 10 ⁻ 9 m

, and

L = 0.900 m

. For the first minimum,

m = 1

Step 4: Rearrange the formula to solve for

y

y = \frac{m}{d} \cdot \frac{λ}{L}

. Substitute the values:

y = \frac{1}{0.260} x 10 ⁻ 3 x \frac{660}{} x 0.900

Step 5: Simplify the expression to find the value of

y

. This will give the distance from the central maximum to the first minimum on the screen. Ensure all units are consistent during the calculation.

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주요 개념

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Double-Slit Experiment

The double-slit experiment demonstrates the wave nature of light through interference patterns created when coherent light passes through two closely spaced slits. The resulting pattern consists of alternating bright and dark fringes on a screen, where bright fringes correspond to constructive interference and dark fringes to destructive interference.

Interference and Path Difference

Interference occurs when two or more waves overlap, leading to a new wave pattern. For the double-slit setup, the path difference between light waves from the two slits determines whether they interfere constructively or destructively. The first minimum occurs where the path difference equals half the wavelength, resulting in destructive interference.

Angular Position of Minima

The angular position of the minima in a double-slit interference pattern can be calculated using the formula sin(θ) = mλ/d, where m is the order of the minimum, λ is the wavelength, and d is the distance between the slits. For the first minimum (m=1), this relationship helps determine the distance from the central maximum to the first minimum on the screen.