Exam 37: Wave Optics

The figure shows two point sources of light,A and B.B emits light waves that are +π radians out of phase with the waves from A.A is 3λ from P.B is 5λ from P.(λ is the wavelength. )The phase difference between waves arriving at P from A and B is

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

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?

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°?

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

Two slits are illuminated with red light (λ = 650 nm).The slits are 0.25 mm apart and the distance to the screen is 1.25 m.What fraction of the maximum intensity on the screen is the intensity measured at a distance 3.0 mm from the central maximum?

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

Nonreflective coatings for camera lenses reduce the loss of light at various surfaces of multi-lens systems,as well as preventing internal reflections that might mar the image.Find the minimum thickness of a layer of magnesium fluoride (n = 1.38)on flint glass (n = 1.66)that will cause destructive interference of reflected light of wavelength λ = 550 nm,a wavelength which is near the middle of the visual spectrum.

Two slits separated by 0.10 mm are illuminated with green light (λ = 540 nm).Calculate the distance (in cm)from the central bright-region to the fifth bright band if the screen is 1.0 m away.

Ray says that interference effects cannot be observed with visible light because random phase changes occur in time intervals less than a nanosecond.Stacy says that doesn't matter if collimated light from a single source reaches multiple openings.(They are arguing about a light source 50.0 cm away from two 0.010 0 mm-wide slits,2.00 mm apart,with a screen 1.00 m away from the slits. )Which one,if either,is correct,and why?

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°. )

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. )

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?

Two slits are illuminated with green light (λ = 540 nm).The slits are 0.05 mm apart and the distance to the screen is 1.5 m.At what distance (in mm)from the central maximum on the screen is the average intensity 50% of the intensity of the central maximum?

Monochromatic light (λ = 500 nm)is incident on a soap bubble (n = 1.40).How thick is the bubble (in nm)if destructive interference occurs in the reflected light?

Bright and dark fringes are seen on a screen when light from a single source reaches two narrow slits a short distance apart.The locations of bright and dark fringes can be interchanged if a thin film is placed in front of one of the slits.The minimum thickness of this film must be

Bright and dark fringes are seen on a screen when light from a single source reaches two narrow slits a short distance apart.The number of fringes per unit length on the screen can be doubled

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 =

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

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