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

Lesson

Young’s experiment and diffraction

Part 2 — the experiment that convinced physicists that light is a wave, and the spreading of light through a single narrow slit.

In this lesson you will

Use the fringe-width expression β = λD/d to solve problems on Young’s double-slit experiment
Predict how the fringe pattern changes with wavelength, distances and the medium
Describe single-slit diffraction and the width of its central maximum

Fringe spacing drawn to scale for λ = 600 nm, d = 0.30 mm, D = 1.5 m (β = 3.0 mm).

Diagram

The double-slit set-up

Fringe spacing drawn to scale for λ = 600 nm, d = 0.30 mm, D = 1.5 m (β = 3.0 mm).

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

S₁ and S₂ lie on the same wavefront from S, so they are coherent.
At a point a distance $y$ from the centre of the screen, the path difference is $\Delta = \dfrac{yd}{D}$ (used, not derived).
The central point is equidistant from both slits: always bright.

Concept

Fringe positions and fringe width

Bright where $\dfrac{yd}{D} = n\lambda$ , dark where $\dfrac{yd}{D} = (n + \tfrac{1}{2})\lambda$ : $y_n = \dfrac{n\lambda D}{d},\qquad y'_n = \left(n + \tfrac{1}{2}\right)\dfrac{\lambda D}{d},\qquad \beta = \dfrac{\lambda D}{d}$

Bright and dark fringes are equally spaced and equally wide.
Angular fringe width $\theta = \beta/D = \lambda/d$ , independent of $D$ .

double slit: equally bright, equally spaced fringes

Bright fringes at y = nβ, dark fringes at y = (n + ½)β.

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