Light of wavelength 500 nm falls normally on a single slit of width 0.20 mm. A screen is placed 2 m from the slit and extends from −22 mm to +22 mm relative to the centre of the pattern. How many diffraction minima are visible on the screen?
Physics · Wave Optics · diffraction of light
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Question

Light of wavelength 500 nm falls normally on a single slit of width 0.20 mm. A screen is placed 2 m from the slit and extends from −22 mm to +22 mm relative to the centre of the pattern. How many diffraction minima are visible on the screen?

Physics · Wave Optics · diffraction of light

G1 Physics · Accepted Answer

For small angles, the position of the m-th minimum is y(m) = mλD ÷ a, where m = ±1, ±2, ±3, ... First calculate the spacing between consecutive minima on one side: λD ÷ a = 500×10⁻⁹×2 ÷ (0.20×10⁻³) = 5×10⁻³ m = 5 mm. Thus the minima occur at ±5 mm, ±10 mm, ±15 mm, ±20 mm, ±25 mm, ... The screen extends only to ±22 mm. Therefore the visible minima are ±5, ±10, ±15 and ±20 mm. That gives 8 minima. Hence the answer is 8.