Exam 35: Diffraction and Interference

The figures below represent interference fringes. The distances from the screen to the slits is the same for each figure, and the planes of the screen and the slits are parallel. In each figure the spacing d between the slits is the same. Which figure(s) represent(s) slits illuminated with light of the shortest wavelength λ? The white spaces represent the interference maxima.

The electric fields arriving at a point P from three coherent sources are described by E₁ = E₀ sin ωt, E₂ = E₀ sin (ωt + π/4) and E₃ = E₀ sin (ωt + π/2). Assume the resultant field is represented by Ep = ER sin (ωt + α). The amplitude of the resultant wave at P is

A planar cross section through two spherical waves emanating from the sources S₁ and S₂ in the plane is shown in the figure. S₁ and S₂ are in phase. The black circles are one and two wavelengths from their respective sources. The lighter circles are one half and one and a half wavelengths distant from their respective sources. If the waves shown arriving at P₂ both arrive with amplitude A, the resultant amplitude at point P₂ is

Each pattern shown below would appear on a screen when monochromatic light of wavelength λ first passes through a narrow slit of width a and then strikes a screen. The darkest areas on the page represent the brightest areas on the screen. In which case does the slit have the greatest width?

A laser beam (λ = 694 nm) is incident on two slits 0.100 mm apart. Approximately how far apart (in m) will the bright interference fringes be on the screen 5.00 m from the double slits?

Light from a helium-neon laser (λ = 632.8 nm) is incident upon a 0.200-mm-wide slit. Find the total width of the central maximum 2.00 m from the slit.

A planar cross section through two spherical waves emanating from the sources S₁ and S₂ in the plane is shown in the figure. The black circles are one and two wavelengths from their respective sources. The lighter circles are one-half and one-and-a-half wavelengths distant from their respective sources. If the phase at S₁ and S₂ is zero at this instant, and the waves shown arriving at P₂ both arrive with amplitude A, the difference in phase angle at point P₂ (in radians) is ​ ​

In a double-slit experiment, the distance between the slits is 0.2 mm and the distance to the screen is 100 cm. What is the phase difference (in degrees) between the waves from the two slits arriving at a point 5 mm from the central maximum when the wavelength is 400 nm? (Convert your result so the angle is between 0 and 360°.)