Wave Optics: Diagram-Based Questions (3)

Question

In Young’s double-slit experiment, the slit separation is $d = 0.5$ mm and the screen is $D = 1.0$ m away. Light of wavelength $\lambda = 600$ nm is used. Find (a) the fringe width, and (b) the distance from the central maximum to the third bright fringe.

Solution — Step by Step

Why This Works

Path difference between the two slits to a point at distance $y$ from the central axis (small angle approximation): $\Delta = y d / D$. Bright fringes occur when $\Delta = n\lambda$, giving $y_n = n\lambda D / d$. Consecutive fringes are separated by $\lambda D / d = \beta$.

The small-angle approximation is valid as long as $y \ll D$, which is true for typical YDSE setups.

Alternative Method

Use the angular fringe width $\theta = \lambda / d$ directly. The linear fringe width on screen is $\beta = D \theta$, giving the same result. Useful when the question specifies angles instead of screen distance.

Common Mistake

Students forget that the third bright fringe is at $y_3 = 3\beta$, not $y_3 = 3.5\beta$ or some other value. Bright fringes are at integer multiples of $\beta$ ($n = 0, 1, 2, ...$); dark fringes are at half-integer multiples ($(n + 1/2)\beta$). Don’t mix these up.