Exam 37: Wave Optics

Two slits separated by 0.050 mm are illuminated with green light (λ = 540 nm). How many bands of bright lines are there between the central maximum and the 12-cm position? (The distance between the double slits and the screen is 1.0 m.)

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.

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

Monochromatic light (λ = 500 nm) is incident on a soap bubble (n = 1.4) that is 50 mm thick. What is the change of phase of the light reflected from the front surface?

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?

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?

For small angle approximations

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

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

A soap bubble (n = 1.35) is floating in air. If the thickness of the bubble wall is 115 nm, what visible light wavelength is most strongly reflected?

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 halved

Suppose two flat glass plates 30-cm long are in contact along one end and separated by a human hair at the other end. If the diameter of the hair is 50 μm, find the separation of the interference fringes when the plates are illuminated by green light, λ = 546 nm.

The bright and dark bands you see in a photograph of a double slit interference pattern represent

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?

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.

In a Newton's rings apparatus, find the phase difference (in radians) when an air wedge of 500 nm thickness is illuminated with red light (λ = 640 nm).

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

In an interference pattern, the wavelength and frequency are

The figure shows two point sources of light, A and B, that emit light waves in phase with each other. A is distant 3λ from point P. B is distant 5λ from P. (λ is the wavelength.) The phase difference between the waves arriving at P from A and B is

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?