Optics

Light interference — Young’s experiment

Two coherent slits produce equally spaced bright and dark fringes; the fringe spacing i = λD/a can be used to determine wavelength.

i = \frac{\lambda D}{a}

Definition: Interference conditions

For slit separation a and screen distance D (D ≫ a), at transverse coordinate y small compared with D, the path difference is approximately δ = ay/D. Bright fringes occur at δ = mλ and dark fringes at δ = (m + 1/2)λ, for integer m.

Adjust wavelength, slit separation, and screen distance to view the screen fringes and intensity profile; the readout uses nm, mm, and m consistently.

Model and quantities

Example: Measuring wavelength from fringes

Monochromatic light passes through slits separated by a = 0.50 mm. The screen is D = 2.0 m away, and adjacent bright fringes are 2.4 mm apart. Find the wavelength.

Solution

λ = ia/D = (2.4×10⁻³ m)(0.50×10⁻³ m)/(2.0 m) = 6.0×10⁻⁷ m = 600 nm.

Quick check

Bright and dark fringes arise when coherent waves superpose: maxima occur for path difference $\Delta=m\lambda$ , minima for $\Delta=(m+1/2)\lambda$ . In the double-slit experiment, for slit separation $a$ , screen distance $D$ , and small angles, fringe spacing is $i=\lambda D/a$ . With $\lambda=600$ nm, $D=2$ m, and $a=0.30$ mm, the spacing is 4 mm. The slits should be illuminated by the same monochromatic source so their phase difference remains stable; changing colour changes the spacing in proportion to wavelength.Measure across several fringes and divide by their number to reduce error. With an incoherent source, rapidly varying phase washes out the pattern.Fringe contrast also depends on the relative intensities of the two beams.

In Young’s experiment, doubling slit separation a while keeping λ and D fixed makes the fringe spacing:

With a and D unchanged, using a longer wavelength makes the fringe spacing:

References

David Halliday, Robert Resnick, Jearl Walker (2018). Fundamentals of Physics