Wave Optics — Part 2: Young’s double slit and single-slit diffraction: visual lesson, ISC Class 12 Physics

Lesson

Young’s Double Slit and Single-Slit Diffraction

Part 2 — two slits give equally spaced fringes; one slit spreads light into a broad central band.

In this lesson you will

Derive the positions of bright and dark fringes and the fringe width β = λD/d in Young’s experiment
Sketch and interpret the intensity distribution of the double-slit pattern
Describe single-slit diffraction (minima a sin θ = nλ, secondary maxima) and find the angular and linear width of the central maximum

Worked examples 4 and 6 drawn to the same scale.

Diagram

Young’s arrangement

Light from a narrow slit S falls on two narrow slits S₁ and S₂, a distance $d$ apart, equidistant from S. Fringes form on a screen a distance $D$ away ( $D \gg d$ ).

S₁ and S₂ are lit by the same wavefront, so they are coherent and in phase.
O, opposite the midpoint of the slits, is equidistant from both: the central fringe is bright.

Concept

The path difference d sin θ

For a point P at height $y$ , draw S₁N perpendicular to S₂P. Since $D \gg d$ , S₁P and NP are almost equal, so the path difference is $\Delta = S_2P - S_1P \approx S_2N = d\sin\theta$ For small angles $\sin\theta \approx \tan\theta = y/D$ , so $\Delta = \dfrac{yd}{D}$ .

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