Diffraction Practice Problems

The refractive index of a newly developed material can be approximated by the equation n(λ) = A/λ^0.5, where λ is the wavelength of light in nanometers and A is a constant equal to 37.6 nm^0.5. A 200 nm thick layer of the material is deposited on a glass substrate (n = 1.55). Determine the wavelengths of visible light that exhibit constructive interference between the reflected waves from the top and bottom interfaces of the thin layer.

Two microscopic slides are in contact at one end and separated by a piece of paper at the other end. Determine the angle of the wedge formed if a monochromatic light of wavelength 528 nm is incident on the slides. There are 12 interference fringes per cm.

A lens made of a material with a refractive index of 1.80 is coated with a thin layer of transparent optical material with a refractive index of 1.70. Calculate the slightest layer that produces the maximum interference at a wavelength of 540 nm.

A student wants to determine the refractive index of an unknown liquid. The student uses an experimental setup that includes a remote control emitting a 12.1 GHz wave, a microwave detector, and a flask containing the liquid. The wave is directed toward the flask, and the reflected signal is measured using the microwave detector. The maximum reflected signal is obtained only when the height of the liquid in the flask is 2.43 cm and 3.34 cm, and no other maximum is found between these two heights. Using the information provided, compute the refractive index of the unknown liquid.

A thin film of magnesium fluoride (MgF₂) is deposited onto a glass substrate. The refractive index of MgF₂ is lower than that of the substrate. The thickness of the film was controlled to be 630 nm. When a beam of light of wavelength 580 nm illuminates the film, the reflected light is at its maximum intensity. And when a beam of light of wavelength 696 nm illuminates the film, the reflected light is at its minimum intensity. Calculate the refractive index of MgF₂.

A diffraction grating is used with a laser that emits light with a monochromatic wavelength of 632.8 nm. The grating has 555 grooves/mm. The laser light is incident at an angle of 35° and diffracted by the grating at an angle of θ. Determine the angles θ_m at which the primary maxima of the diffraction pattern will be observed.

Your science teacher asks you to generate a circular diffraction pattern using coherent light of wavelength 486 nm and a circular aperture of radius 0.051 mm. The width of the central maximum on the screen should be 5.5 mm. What is the necessary distance between the aperture and the screen to obtain this diffraction pattern?

A photographer is using a telephoto lens to capture pictures of birds. If the camera lens has an 85 mm focal length, and the aperture is fully opened to 34 mm, determine what the f-number of this telephoto lens will be.

A sodium-vapor lamp illuminates a diffraction grating that is positioned 1.23 meters away from a viewing screen. Light emitted at a wavelength of 589 nm produces a second-order bright fringe 30.31 cm away from the central maximum on the viewing screen. Determine the wavelength of the emitted light that produces a second-order bright fringe positioned 42.42 cm away from the central maximum on the viewing screen.

Calculate the angle of the first dark fringe (in radians and in degrees) observed in a diffraction pattern when a light of wavelength 1.54 μm is directed toward a pinhole of radius 0.065 mm.

A helium-neon laser of wavelength 632.8 nm is used with a Michelson interferometer. When the movable mirror of the interferometer is displaced by 0.85 mm, m bright fringes are observed to move past a reference line. Determine the number of fringes 'm'.

An argon-ion laser of wavelength 514 nm is used with a Michelson interferometer. In one arm, the laser light passes through a cubic glass chamber with a side of 3.0 cm. The glass chamber in the interferometer is initially evacuated. A bright fringe is located at the reference line. The gas chamber is then filled with nitrogen gas at atmospheric pressure. Determine the number of fringes that you will count while moving past the reference line when the glass chamber is filled with nitrogen. The refractive index of nitrogen at standard atmospheric conditions is 1.00029.

A monochromatic beam of wavelength 532 nm is incident on a circular hole. When a whiteboard serving as the viewing screen is positioned 2.5 m behind the hole, a circular diffraction pattern is observed with a central maximum width of 1.8 cm. Determine the radius of the hole.

An emerging class of two-dimensional material termed MXene has a c-lattice parameter (interplanar spacing) of 9.23 Å. If the electromagnetic ray is made incident on the planes at an angle of 30°, determine its wavelength for the first interference maximum. Also, determine the region in which the electromagnetic ray falls in terms of its wavelength.

In a lab experiment, a diffraction grating is used to study light patterns. The second-order maximum for the diffraction pattern appears at an angle of 30.0°. Determine the angle at which the third-order maximum would occur.

Consider an atom that absorbs radiation at wavelengths of 165 nm, 320 nm, and 510 nm from the ground state. What other wavelengths can be emitted? Take the ground state energy to be 0 eV.