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 8

35장, 문제 8

Coherent light with wavelength 450 nm falls on a pair of slits. On a screen 1.80 m away, the distance between dark fringes is 3.90 mm. What is the slit separation?

검증된 단계별 안내

Step 1: Understand the problem. The problem involves a double-slit interference pattern. The distance between dark fringes corresponds to the distance between adjacent minima in the interference pattern. The formula for the position of minima is given by:

y = \frac{m}{d} \cdot \frac{λ}{L}

, where

y

is the distance between adjacent minima,

λ

is the wavelength of light,

L

is the distance to the screen, and

d

is the slit separation.

Step 2: Rearrange the formula to solve for the slit separation

d

. The formula becomes:

d = \frac{λ}{\frac{y}{L}}

. This equation relates the slit separation to the wavelength, the distance between adjacent minima, and the distance to the screen.

Step 3: Convert all given quantities into SI units. The wavelength

λ

is given as 450 nm, which is

450 \times 10^{- 9} m

. The distance between dark fringes

y

is 3.90 mm, which is

3.90 \times 10^{- 3} m

. The distance to the screen

L

is 1.80 m.

Step 4: Substitute the known values into the rearranged formula. Using

λ = 450 \times 10^{- 9}

y = 3.90 \times 10^{- 3}

, and

L = 1.80

, the formula becomes:

d = \frac{450}{\times} \div 3.90 \times 10^{- 3} m

Step 5: Simplify the expression to find the value of

d

. Perform the arithmetic operations to calculate the slit separation. Ensure that the units are consistent throughout the calculation, and the final result will be in meters.

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주요 개념

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Young's Double Slit Experiment

This experiment demonstrates the wave nature of light through the interference pattern created by coherent light passing through two closely spaced slits. The resulting pattern consists of alternating bright and dark fringes on a screen, which can be analyzed to determine properties such as slit separation and wavelength.

Interference Pattern

An interference pattern is formed when waves overlap, leading to regions of constructive interference (bright fringes) and destructive interference (dark fringes). The positions of these fringes depend on the wavelength of the light, the distance between the slits, and the distance to the screen, which can be mathematically described using the interference formula.

Slit Separation and Fringe Spacing

The distance between the slits, known as slit separation, directly influences the spacing of the interference fringes on the screen. The relationship between the slit separation, wavelength, and the distance to the screen can be expressed through the formula for fringe spacing, allowing for the calculation of slit separation when fringe distance and other parameters are known.