Condition for interference fringes

In Young’s double slit experiment, the bright and dark fringes are loci of points on the screen where the path difference between light from the two slits is constant.

If the two slits are at $S_1$ and $S_2$, then for any point $P$ on the screen, $S_2P - S_1P = \text{constant}.$

Geometrical meaning of constant path difference

The locus of a point for which the difference of distances from two fixed points is constant is a hyperbola.

Since $S_1$ and $S_2$ act like the two fixed points (foci), the interference fringes are, in general, hyperbolic.

Why they often appear straight in textbooks

In the usual YDSE arrangement, the screen is placed far from the slits and the angles are small. Under this approximation, small portions of these hyperbolae look like straight, equally spaced lines.

But the actual geometrical shape is still hyperbola.

Evaluate the options

• A: circle — Incorrect
• B: hyperbola — Correct
• C: parabola — Incorrect
• D: straight line — Only an approximation in the usual setup, not the true shape

Final answer

Therefore, the shape of interference fringes formed on the screen is $\boxed{\text{hyperbola}}.$

Comparison with stored correct answer

The stored correct answer is D (straight line).

However, the exact geometrical shape of the fringes in YDSE is hyperbola. Straight fringes are obtained only as an approximate appearance under small-angle/far-screen conditions.

Hence, I disagree with the stored answer.