Exam 27: Wave Optics

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 $\degree$ relative to the central peak,and the wavelength is 500 nm? (Convert your result so the angle is between 0 and 360 $\degree$ . )

Suppose a 5.0-meter diameter telescope were constructed on the dark side of the moon.The viewing there (except for brief periods of sunlight)would be excellent.As an example,what would be the separation between two objects that could just be resolved on the planet Mars in 500 nm light? [The distance to Mars at closest approach is 50 million miles.]

A binary star system in the constellation Orion has an angular separation between the two stars of 1.2 *10 ^{- 5} radians.If $\lambda$ = 5 *10 ^{- 7} m,what is the smallest aperture (diameter)telescope that may be used to resolve the two stars?

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

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 $\degree$ . )

Monochromatic light ( $\lambda$ = 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 $\degree$ and 360 $\degree$ ?

At what distance could one theoretically distinguish two automobile headlights separated by 1.5 meters? Assume a pupil diameter of 0.50 cm and yellow headlights seen at the wavelength 5.0 *10 ^{- 7} m.Assume eye fluid has an average n = 1.33.

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 $\lambda$ = 450 nm and a brightness minimum at $\lambda$ = 600 nm.What is the thickness of the oil film?

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 $\lambda$ = 550 nm,a wavelength which is near the middle of the visual spectrum.

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 $\mu$ m,find the separation of the interference fringes when the plates are illuminated by green light, $\lambda$ = 546 nm.

Monochromatic light ( $\lambda$ = 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?

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

A narrow slit is illuminated with sodium yellow light of wavelength 589 nm.If the central maximum extends to $\pm$ 30.0 $\degree$ ,how wide is the slit?

Each pattern shown below would appear on a screen when monochromatic light of wavelength $\lambda$ 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?

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

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

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

Each pattern shown below would appear on a screen when monochromatic light of wavelength $\lambda$ 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 narrowest width?

In a double-slit experiment,the distance between the slits is 0.2 mm,and the distance to the screen is 150 cm.What wavelength (in nm)is needed to have the intensity at a point 1 mm from the central maximum on the screen be 80% of the maximum intensity?

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 $\lambda$ in air is