All Problems

Interference of Light

Problem 5.71

Figure 5.14 illustrates the interference experiment with Fresnel mirrors. The angle between the mirrors is α=12,\alpha=12^{\prime}, the distances from the mirrors' intersection line to the narrow slit SS and the screen ScS c are equal to r=10.0 cmr=10.0 \mathrm{~cm} and b=130 cmb=130 \mathrm{~cm} respec tively. The wavelength of light is λ=0.55μm.\lambda=0.55 \mu \mathrm{m} . Find: (a) the width of a fringe on the screen and the number of possible maxima; (b) the shift of the interference pattern on the screen when the slit is displaced by δl=1.0 mm\delta l=1.0 \mathrm{~mm} along the arc of radius rr with centre at the point OO; (c) at what maximum width δmax\delta_{\max } of the slit the interference fringes on the screen are still observed sufficiently sharp.

Reveal Answer
5.71. (a) Δx=λ(b+r)/2αr=1.1 mm,9\Delta x=\lambda(b+r) / 2 \alpha r=1.1 \mathrm{~mm}, 9 maxima; (b) the shift is δx=(b/r)δl=13 mm;\delta x=(b / r) \delta l=13 \mathrm{~mm} ; (c) the fringe pattern is still sharp when δxΔx/2,\delta x \leqslant \Delta x / 2, hence δmax=(1+r/b)λ/4α=43μm.\delta_{\max }=(1+r / b) \lambda / 4 \alpha=43 \mu \mathrm{m} .