Interference (CIE A Level Physics)

A student designs an experiment to replicate Young’s double-slit demonstration. 

The student uses a candle as a light source, with a piece of coloured filter paper to produce monochromatic light. They consider additional apparatus required to observe an interference pattern. 

Sketch a diagram of the experimental setup the student should use to observe an interference pattern.

Label all apparatus and relevant measurements to be taken.

The student labels the two slits on the double-slit grating slit X and slit Y. 

The student then paints over slit X, such that the intensity of light emerging from it is 50% of the intensity emerging from slit Y. 

Discuss the effects, if any, this will have on the student’s observations.

The student finishes setting up their apparatus and makes a quick note of two separate measurements in a lab book as shown in Fig. 1.1.  

Fig. 1.1

They then plot a graph of the intensity of light against the distance from the centre of the screen, represented by the origin as shown in Fig. 1.2. 

Fig. 1.2

Determine which colour of filter paper the student most likely chose for this experiment, using the information in Fig. 1.1 and Fig. 1.2.

Determine the phase angle between the waves meeting at the point that is 2.8 mm from the centre of the screen.

Fig. 1.1 shows an arrangement for observing the interference pattern produced by laser light passing through two narrow slits S₁ and S₂.

Fig. 1.1

The distance S₁S₂ is d, and the distance between the double slit and the screen is D, where D ≫ d, so angles θ and ϕ are small.

M is the midpoint of S₁S₂ and it is observed that there is a bright fringe at point A on the screen, a distance f_n from point O on the screen. Light from S₁ travels a distance S₂Y further to point A than light from S₁.

The wavelength of light from the laser is 650 nm and the angular separation of the bright fringes on the screen is 5.00 × 10⁻⁴ rad.

Calculate the distance between the two slits.

A bright fringe is observed at A. 

Deduce expressions for the following angles in the double-slit arrangement shown in part a: 

[2]

[2]

The separation of the slits S₁ and S₂ is 1.30 mm.

The distance MO is 1.40 m.

The distance f_n is the distance of the ninth bright fringe from O and the angle θ is 3.70 × 10⁻³ radians. 

Calculate the wavelength of the laser light.