(II) Light of wavelength 680 nm falls on two slits and produces an interference pattern in which

step 1 All right, so the fringe angle theta is just tan theta is equal to x over l, x being the separat

(II) Light of wavelength 680 nm falls on two slits and...

(II) Light of wavelength 680 $\mathrm{nm}$ falls on two slits and
produces an interference pattern in which the third-order
bright fringe is 38 $\mathrm{mm}$ from the central fringe on a screen
2.6 $\mathrm{m}$ away. What is the separation of the two slits?

Key Concepts

Constructive Interference

Constructive interference is the process where light waves align in phase such that their amplitudes add together, producing bright fringes. It occurs when the path difference between the waves is an integer multiple of the wavelength.

Path Difference and Fringe Order

The path difference between waves from the two slits, which determines the interference pattern, is related to the fringe order. For each order of fringe, a specific multiple of the wavelength is involved. This concept explains why higher order bright fringes appear at larger distances from the central maximum.

Young's Double-Slit Experiment

This experiment demonstrates the wave nature of light by showing how two coherent light sources produce an interference pattern of alternating bright and dark fringes. It is fundamental in explaining how light waves superpose and interfere, thereby confirming the wave theory of light.

Interference of Waves

Interference occurs when two or more coherent waves overlap, leading to regions of constructive interference (bright fringes) where the waves reinforce each other, and regions of destructive interference (dark fringes) where they cancel out. This basic phenomenon is central to understanding patterns produced in many optical experiments.

Fringe Spacing Formula

The fringe spacing in a double-slit interference pattern is determined by the relationship between the wavelength of the light, the distance from the slits to the screen, and the separation of the slits. The formula m? = (d sin ?) or its small-angle approximation links these parameters and is used to determine unknown quantities in the experiment.

Transcript

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