Blue light of wavelength λpasses through a single slit of width w . A diffraction pattern appear

step 1 This is a single slit diffraction problem. So 2x equals 2 lambda Lm over W. So if lambda goes to

Blue light of wavelength λpasses through a single slit of...

Blue light of wavelength $\lambda$ passes through a single slit of width $w .$ A diffraction pattern appears on a screen. If you now replace the blue light with a green light of wavelength $1.5 \lambda$, to what width should you change the slit to get the original pattern back?

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Key Concepts

Single-Slit Diffraction

Single-slit diffraction refers to the spreading of light waves as they pass through a narrow aperture, resulting in an interference pattern of bright and dark fringes on a screen. This phenomenon highlights the wave nature of light and the way in which aperture size influences the distribution of light intensity.

Diffraction Condition and Minima Positions

The positions of the dark fringes (minima) in a single-slit diffraction pattern are determined by the condition sin? = m?/w, where m is an integer (not equal to zero), ? is the wavelength of the light, and w is the width of the slit. This condition establishes how changes in the wavelength or slit width affect the angular positions of the minima.

Scaling Relation Between Wavelength and Slit Width

To maintain the same diffraction pattern when the wavelength changes, the ratio of the wavelength to the slit width (?/w) must remain constant. This scaling relationship means that if the wavelength increases, the slit width must be increased proportionally to preserve the angular positions of the diffraction minima and, consequently, the overall pattern.

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