In Young's double-slit interference experiment, two parallel slits S 1 and S2 are two phase main light sources, the distance between S 1 and S2 is d, and point O is the central bright pattern (Ox) on the observation screen. Whether the point P on the observation screen is bright or dark depends on the optical path difference dsinθ when S 1 and S2 reach the point P ... According to the interference condition of coherent light, when the optical path difference is even multiple of half wavelength (integer multiple of wavelength), bright stripes appear; When the optical path difference is an odd multiple of half wavelength, dark lines will appear. However, different textbooks have different expressions on the quantitative relationship between optical path difference and wavelength. The following are common expressions.

The first expression:

Bright grain dsinθ = 2kλ = kλ

The orderly distribution of interference fringes is shown in Figure 3.

(k=0， 1，2，…)

Figure 3

Distribution of bright and dark stripes and corresponding orderly representation

Dark stripe dsinθ = (2k+ 1) λ

The second expression: bright stripe dsinθ=2kλ=kλ.

(k=0， 1，2，…)

The third expression: dark stripe dsinθ = (2k- 1) λ.

(k= 1，2，3，…)

(k=0， 1，2，…)

The orderly distribution of interference fringes is shown in Figure 4.

Dark stripe dsinθ=(2k+ 1)λ

The third expression: bright grain DSinθ = 2kλ = kλ.

(k=0， 1，2，…)(k= 1，2，3，…)

Dark stripe dsinθ = (2k- 1) λ

Where λ is the wavelength and k is the number of interference fringes.

In the above expressions, the theoretical and experimental results of various expressions of interference fringes are consistent, and they can accurately represent the order distribution of interference fringes. However, the different manifestations of interference dark lines are different. The following are analyzed and discussed respectively.

The first expression: dark stripe dsinθ = (2k+ 1) λ.

2

(k=0， 1，2，…)

Fig. 4 Distribution of bright and dark stripes and corresponding order degree representation.

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Scientific and technological information ○ the frontier of science and education ○ science and; No.32 [2008] of Technical Capital

If the first expression is adopted, two dark lines of level 0 (+0 and -0) appear in the fringe distribution map (Figure 2), which are located on both sides of the central (level 0) light, which does not conform to the expression habit.

If the second expression is adopted, there is a 0-level dark stripe (Figure 3) in the stripe distribution pattern, which is located on one side of the central (0-level) bright stripe, but the corresponding place on the other side of the central (0-level) bright stripe is-1 dark stripe. This expression makes the distribution of dark stripes asymmetric with respect to the central bright stripes.

If the third expression is adopted, the fringe distribution diagram is shown in Figure 4, with only one bright stripe at the center, and the bright stripes and dark stripes at both sides are symmetrically distributed from 1.

It can be seen that the first and second expressions only explain the quantitative relationship between optical path difference and wavelength in theory, without considering whether the theoretical expression conforms to the actual expression habits. The third expression accurately reflects the actual distribution of interference light and dark fringes, which makes the theoretical expression consistent with the actual expression habits. This expression is better.

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