Exam 37: Wave Optics

In a double-slit experiment using light of wavelength 486 nm, the slit spacing is 0.600 mm and the screen is 2.00 m from the slits. Find the distance along the screen between adjacent bright fringes.

When a central dark fringe is observed in reflection in a circular interference pattern, waves reflected from the upper and lower surfaces of the medium must have a phase difference, in radians, of

The superposition of two waves E₁ = E₀ sin(ωt) and E₂ = E₀ sin(ωt + φ) arriving at the same point in space at the same time is E =

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. Which figure(s) represent(s) slits with the smallest spacing d between the slits? The white spaces represent the interference maxima.

Bright and dark fringes are seen on a screen when light from a single source reaches two narrow slits a short distance apart. Each bright fringe will shift to the location of the adjacent bright fringe if a thin film is placed in front of one of the slits. The minimum thickness of this film must be

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 E_p = E_R 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. 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

A uniform film of oil (n = 1.31) is floating on water. When sunlight in air is incident normally on the film, an observer finds that the reflected light has a brightness maximum at λ = 450 nm and a brightness minimum at λ = 600 nm. What is the thickness of the oil film?

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 P₁ both arrive with amplitude A, the magnitude of the phase angle of each wave at point P₁ (in radians) 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 P₁ both arrive with amplitude A, the resultant amplitude at point P₁ is

A film of index of refraction n₁ coats a surface with index of refraction n₂. When n₁ < n₂, the condition for constructive interference for reflected monochromatic light of wavelength λ in air is

Monochromatic light (λ = 500 nm) is incident on a soap bubble (n = 1.40). What is the wavelength of the light (in nm) in the bubble film?

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. Which figure(s) represent(s) slits with the greatest spacing d between the slits? The white spaces represent the interference maxima.

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.

Light is incident on a double-slit. The fourth bright band has an angular distance of 7.0° from the central maximum. What is the distance between the slits (in μm)? (Assume the frequency of the light is 5.4 × 10¹⁴ Hz.)

Monochromatic light (λ = 500 nm) is incident on a soap bubble (n = 1.4) that is 500-nm thick. Calculate the change of phase of the light that penetrates the front surface, reflects from the second surface, and emerges through the first surface as an angle between 0° and 360°?

Estimate the distance (in cm) between the central bright region and the third dark fringe on a screen 5.00 m from two double slits 0.500 mm apart illuminated by 500-nm light.

In a double slit experiment, the distance between the slits is 0.2 mm and the distance to the screen is 150 cm. What is the phase difference (in degrees) between the waves from the two slits arriving at a point P when the angular distance of P is 10° relative to the central peak, and the wavelength is 500 nm? (Convert your result so the angle is between 0 and 360°.)

The light reflected from a soap bubble (n = 1.40) appears red (λ = 640 nm) at its center. What is the minimum thickness (in nm)?

When the adjustable mirror on the Michelson interferometer is moved 20 wavelengths, how many fringe pattern shifts would be counted?