The shape of the interference fringes in Young's double-slit experiment, when the distance between the slit and the screen is very large as compared to the slit-separation, is nearly
The shape of the interference fringes in Young's double-slit experiment, when the distance between the slit and the screen is very large as compared to the slit-separation, is nearly
Options
Correct option: A — straight.
- The locus of a constant path difference between two point slits is a hyperbola.
- When the screen distance D is very large compared to the slit separation, the small central portion of each hyperbola seen on the screen appears as nearly straight, parallel fringes.
Marking Scheme
- 11 mark: correct option A (straight).
- 2Accept the reasoning that fringes are strictly hyperbolic but appear straight and parallel for D slit separation.
Hint
Fringes are loci of constant path difference (hyperbolae); ask how they look on a distant screen over a small central region.
Quick Oral Answer
Fringes are loci of constant path difference, which are hyperbolae; but when the screen is far compared with the slit separation, the observed central fringes look like straight, parallel lines.
Analysis & Explanation
This question distinguishes the exact geometry of interference fringes from their observed appearance.
Concept
- A bright or dark fringe is the set of points where the path difference () is constant. Geometrically, points with a constant difference of distances from two fixed points lie on a hyperbola.
- On a flat screen placed very far from the slits (D slit separation d), only the small region near the centre is observed. Over this small region the hyperbolic curves are so gently curved that the fringes look like equally spaced straight lines parallel to the slits.
Why the distractors are wrong
- D (hyperbolic): true in the strict, full-field sense, but the question asks what the fringes look like in the far-field limit, where they appear straight — so D is not the intended answer.
- B (parabolic) and C (circular): neither matches the constant-path-difference locus; circular fringes arise in different setups (e.g. Newton's rings / Fabry–Perot), not in the standard YDSE geometry.
Exam trap
- The precise answer is 'hyperbolic', but under the stated condition () CBSE expects 'nearly straight'. Read the qualifier 'very large' carefully.
Common Mistakes
- 1Choosing 'hyperbolic' without noting the far-screen condition that makes the fringes appear straight.
- 2Confusing YDSE fringes with the circular fringes of Newton's rings.
- 3Assuming fringes are parabolic by analogy with projectile paths — the locus is hyperbolic, not parabolic.
Interesting Facts
Strictly, each interference maximum lies on a hyperboloid of revolution about the axis joining the two slits; the flat screen slices it into a hyperbola that looks straight near the centre.
Thomas Young first demonstrated these fringes around 1801, providing decisive evidence for the wave nature of light against Newton's corpuscular theory.
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Frequently Asked Questions
Are the fringes truly straight or only approximately straight?
Only approximately. The exact loci of constant path difference are hyperbolae. When the screen is very far compared with the slit separation, only their nearly-straight central portions are seen, so the fringes appear straight and parallel.
Why aren't the fringes circular like Newton's rings?
Circular fringes arise from interference with circular symmetry (e.g. a point/extended source over an air film in Newton's rings). In YDSE, the two slit sources produce constant-path-difference curves that are hyperbolae, appearing straight near the axis.