In a two-slit experiment, monochromatic coherent light of wavelength 600 nm passes through a pair of slits separated by
2.2
×
10
−
5
m. At what angle away from the centerline does the first bright fringe occur?

Question

In a two-slit experiment, monochromatic coherent light of wavelength 600 nm passes through a pair of slits separated by 
2.2
×
10
−
5
m.  At what angle away from the centerline does the first bright fringe occur?

BlackTom AI · Accepted Answer

In a two-slit interference setup, the bright fringes satisfy the condition d sin(θ) = m λ, where d is the slit separation, θ is the angle relative to the central maximum, m is the fringe order, and λ is the wavelength.

First, identify the given quantities: d = 2.2 × 10^−5 m, λ = 600 nm = 6.0 × 10^−7 m, and we want the first bright fringe, so m = 1.

Compute sin(θ) using sin(θ) = m λ / d = (1)(6.0 × 10^−7 m) / (2.2 × 10^−5 m) ≈ 0.0273.

Now approximate θ from sin(θ) ≈ θ for small angles (in radians) or use arcsin directly: θ ≈ arcsin(0.0273) ≈ 0.0273 radians ≈ 1.56 degrees.

Evaluate the answer choices by checking which angle corresponds to the calculation above:
- 4.70°: This would require a larger sin(θ) value; it corresponds to a bigger θ than the first bright fringe predicts. It does not satisfy sin(θ) = λ/d for m = 1.
- 2.22°: This is still larger than the computed 1.56° and does not match arcsin(0.0273). It would imply sin(θ) ≈ 0.0387, not 0.0273.
- 3.12°: Again, this is bigger than the correct value and would imply sin(θ) ≈ 0.0544, inconsistent with λ/d for m = 1.
- 1.56°: This exactly matches the calculated angle from arcsin(λ/d) with m = 1, consistent with the small-angle approximation used here.
- 6.24°: This is far larger and would correspond to a much larger sin(θ), inconsistent with the given λ/d ratio for the first bright fringe.

Thus, among the provided options, the one that aligns with the derived angle is the 1.56° choice, since it satisfies the single-slit-difference interference condition for the first bright fringe (m = 1) with the given d and λ.

In a two-slit experiment, monochromatic coherent light of wavelength 600 nm passes through a pair of slits separated by 2.2 × 10 − 5 m. At what angle away from the centerline does the first bright fringe occur?单项选择题

类似问题

Two thin slits are 0.050 mm apart. Monochromatic light of wavelength 634 nm falls on the slits. If there is a screen 6.0 m away, how far apart are adjacent interference fringes?

A monochromatic light is incident on a Young's double slit setup that has a slit separation of 30.0 μm. The resultant bright fringe separation is 2.15 cm on a screen 1.20 m from the double slit. What is the separation between the third-order bright fringe and the zeroth-order bright fringe?

Which of the following best explains why destructive interference occurs at certain points in a double-slit experiment?

Two slits in a metal barrier are placed in front of a source of microwave radiation. The wavelength of the microwaves is 3.0 cm. The distance ( S1P ) is 90.0 cm and the distance ( S2P ) is 98.0 cm. What is the path difference between the two waves in cm?

A double-slit experiment with 0.20 mm slit separation and 5.0x102 nm light shows the first bright fringe at 3.0 mm. What is the distance to the screen?

Coherent light of wavelength 519 nm passes through two slits. In the resulting interference pattern on a screen 4.6 m away, adjacent bright fringes are 4.0 mm apart. What is the separation of the two slits?

A double-slit interference experiment is performed in the air. Later, the same apparatus is immersed in benzene (which has an index of refraction of 1.50), and the experiment is repeated. When the apparatus is in benzene, you observe that the interference fringes are

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单