   Chapter 27, Problem 18PE

Chapter
Section
Textbook Problem

Figure 27.56 shows a double slit located a distance x from a screen, with the distance from the center of the screen given by y. When the distance d between the slits is relatively large, there will be numerous bright spots, called fringes. Show that, for small angles (where sin θ ≈ θ , with θ in radians), the distance between fringes is given by Δ y = x λ / d . Figure 27.56 The distance between adjacent fringes is Δ y = x λ / d , assuming the slit separation d is large compared with λ .

To determine

To Show:

The distance between fringes is given by Δy=xλd

Explanation

Given info:

Figure shows a double slit located a distance x, from a screen, with the distance from a screen, with the distance from the center of the screen given by y . When the distance d between the slits is relatively large, there will be numerous bright spots.

Formula used:

For two adjacent fringes we have,

dsinθm=mλanddsinθm+1=(m+1)λ

Calculation:

Subtracting these equations gives

dsinθm=mλandd(sinθm+1sinθ)=[(m+1)m]

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