Questions: Fringe Spacing in Interference Patterns

Question 1

In a double-slit experiment, the slit separation d is doubled while wavelength and screen distance are held constant. What happens to the fringe spacing?

• A. It doubles — wider slits spread the pattern out
• B. It halves — fringes crowd together when slits are farther apart
• C. It stays the same — slit separation does not affect fringe spacing
• D. It quadruples — fringe spacing scales with d²

Answer: (B)

From Δy = λD/d, doubling d halves the fringe spacing. This surprises many students who expect wider-apart slits to spread the fringes out (by analogy with a wider spray). The logic runs the other way: when slits are farther apart, only a tiny angle is needed for the path difference to reach one full wavelength, so fringes are compressed. The key insight is that d is in the denominator.

Question 2

A double-slit experiment uses slits separated by d = 0.50 mm and a screen at D = 1.5 m. The observed fringe spacing is Δy = 1.5 mm. What wavelength does this imply?

• A. 250 nm — visible violet
• B. 500 nm — visible green
• C. 750 nm — near infrared
• D. 1500 nm — infrared, outside visible range

Answer: (B)

Rearranging Δy = λD/d gives λ = Δy·d/D = (1.5×10⁻³ m × 0.50×10⁻³ m) / 1.5 m = 5.0×10⁻⁷ m = 500 nm — green light. This calculation shows how early experimenters used fringe measurements to determine wavelengths of visible light from purely geometric measurements.

Question 3

Increasing the distance D between the double-slit and the screen makes the fringes wider.

• T. True
• F. False

Answer: True

Yes — from Δy = λD/d, fringe spacing is directly proportional to D. Moving the screen farther away amplifies any angular spacing into greater physical separation. The fringes get broader without the pattern itself changing; you are just projecting it onto a more distant surface.

Question 4

Using a longer-wavelength (red) light source instead of a shorter-wavelength (blue) source will make the fringes closer together in a double-slit experiment.

• T. True
• F. False

Answer: False

Longer wavelength produces wider fringe spacing — λ is in the numerator of Δy = λD/d. Red light (λ ≈ 700 nm) produces broader fringes than blue light (λ ≈ 450 nm) under the same geometry. This is why white-light double-slit patterns show different colors offset from each other: each wavelength has its own spacing.

Question 5

How can the fringe-spacing formula Δy = λD/d be used to measure an unknown wavelength of light, and which quantities must be measured experimentally?

Model answer: Rearranging gives λ = Δy·d/D. The experimentally measured quantities are the fringe spacing Δy (measured on the screen), the slit separation d (known from the apparatus), and the slit-to-screen distance D (measured with a ruler). Plugging these in yields the wavelength.

This is how early experimenters determined visible light wavelengths well before quantum theory — purely from geometry and a measured fringe pattern. The same relationship runs in reverse in modern spectroscopy: known wavelengths calibrate the geometry of the apparatus.