You are given a slide with two slits cut into it and asked...

You are given a slide with two slits cut into it and asked how far apart the slits are. You shine white light on the slide and notice the first-order color spectrum that is created on a screen $3.40 \mathrm{~m}$ away. On the screen, the red light with a wavelength of $700 \mathrm{~nm}$ is separated from the violet light with a wavelength of $400 \mathrm{~nm}$ by $7.00 \mathrm{~mm}$. What is the separation of the two slits?

Key Concepts

Wavelength Dependence in Interference

Different wavelengths of light produce interference patterns with different fringe spacings. In experiments using multi-wavelength light, such as white light, variations in fringe positions for different colors provide insights into the dispersion of light. This relationship is crucial in determining parameters like slit separation by comparing how the fringe positions shift with wavelength.

Small Angle Approximation

When the angles involved in a diffraction or interference experiment are small, the sine and tangent of the angle can be approximated by the angle itself (in radians). This simplifies the mathematical treatment of the problem by allowing linear relationships between the fringe position, wavelength, and slit separation, making experimental calculations more straightforward.

Double-Slit Experiment

The double-slit experiment demonstrates the wave nature of light by showing that light passing through two narrow, closely spaced slits produces an interference pattern on a screen. This phenomenon arises from the constructive and destructive interference of the light waves emerging from each slit, confirming that light exhibits wave-like properties.

Interference Fringe Spacing

Interference fringe spacing refers to the distance between consecutive bright (or dark) fringes in an interference pattern. This spacing is determined by the wavelength of the light, the separation between the slits, and the distance from the slits to the screen. The relation is often given by an equation where the fringe location is proportional to the wavelength and screen distance and inversely proportional to the slit separation.

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