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 fn 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.
Deduce expressions for the following angles θ in terms of S2Y and d in the double-slit arrangement shown in part a.
[2]
Calculate the distance S1S2 between the two slits.
In a different experimental set up the separation of the slits S1 and S2 is 1.30 mm.
The distance MO is 1.40 m.
The distance fn is the distance of the ninth bright fringe from O and the angle φ is 3.70 × 10−3 radians.
Calculate the wavelength of the laser light.
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