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Young's Double-Slit Experiment and Fringe Width

Young's double-slit experiment demonstrates interference of light using two coherent sources, producing alternate bright and dark fringes on a screen. The fringe width is beta = λ D/d.

In one line: Wider screen distance widens fringes; wider slit separation squeezes fringes.

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Understand it

  • Two narrow slits act as coherent sources when they are derived from the same source.
  • At a point on the screen, waves from the two slits superpose.
  • If the path difference is n λ, a bright fringe is formed.
  • If the path difference is (n + 1/2) λ, a dark fringe is formed.
  • Fringe width is the distance between two consecutive bright fringes or two consecutive dark fringes.

Example

If red light is replaced by blue light in the same setup, the wavelength decreases, so the fringe width decreases and fringes come closer.

Formula and rule

Fringe width: beta = λ D/d. beta, λ, D and d are in metre in SI units.

Bright fringe: path difference = n λ.

Dark fringe: path difference = (n + 1/2) λ.

The formula is valid when D is much larger than d and the slits are coherent and narrow.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

In YDSE, λ = 600 nm = 6.0 × 10−7 m, D = 1.5 m and d = 0.30 mm = 3.0 × 10−4 m.

  1. 1Fringe width beta = λ D/d = (6.0 × 10−7 m x 1.5 m)/(3.0 × 10−4 m) = 3.0 × 10−3 m = 3.0 mm.
  2. 2The second bright fringe from the centre is at y2 = 2 beta = 6.0 mm, while the first dark fringe is at beta/2 = 1.5 mm from the central bright fringe.

Method you can reuse

  1. 1Identify λ, D and d, convert all to SI units, use beta = λ D/d, calculate beta, then interpret whether the change makes fringes closer or farther apart.
  2. 2For fringe position questions, apply path difference conditions for bright and dark fringes.

Sketch it in your answer

Draw source, two slits S1 and S2, screen at distance D, a point P at distance y from the central line, slit separation d, path difference and central bright fringe O.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What happens to the fringe width in YDSE if the screen is moved farther away from the slits?

Think first, then show answer
The fringe width increases because beta = λ D/d. When D increases while wavelength and slit separation remain constant, the spacing between consecutive bright or dark fringes becomes larger.

Common wrong answer

The central fringe is dark because the two paths are different.

Why it loses marks: At the central point, path difference is zero, so constructive interference gives a bright fringe.

Don't mix this up

Students often use slit width instead of slit separation in beta = λ D/d. In this formula, d is the distance between the two slits, not the width of each slit.

Exam tip

Always convert nanometres to metres and centimetres or millimetres to metres before substitution. State whether the point is bright or dark by checking path difference.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

It is asked through fringe-width numericals, identifying bright or dark positions, explaining coherent sources, and predicting changes when λ, D or d is changed.
  1. 1

    Enough for 1 mark

    Young's double-slit experiment demonstrates interference of light using two coherent sources, producing alternate bright and dark fringes on a screen. The fringe width is beta = λ D/d.

  2. 2

    Add for 2 marks

    Example: If red light is replaced by blue light in the same setup, the wavelength decreases, so the fringe width decreases and fringes come closer.

  3. 3

    Add for 3 marks

    Two narrow slits act as coherent sources when they are derived from the same source.

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