Single Slit Diffraction Practice Problems

An astronomer uses a telescope with a magnification of 31x and has an objective lens with a radius of 11 cm. To ensure he captures all the light rays from a distant star directly along the telescope's optical axis, what should be the minimum diameter value of the eyepiece's lens?

An aperture is illuminated with a beam of light of wavelength 550 nm. The light intensity pattern observed on a screen positioned 2.0 m behind the aperture is shown below. Identify the type of the aperture based on the observed pattern.

A beam of coherent light of wavelength 488 nm illuminates an aperture. The light intensity pattern observed on a screen positioned 2.8 m behind the aperture is shown below. Is the aperture a single slit or a double slit? If the observed pattern corresponds to a single-slit diffraction pattern, what is the width of the slit? Alternatively, what is the distance between the two slits if the pattern indicates a double-slit interference pattern?

Laser light exhibits coherence due to properties such as phase alignment, directional uniformity, consistent polarization, and nearly identical wavelengths, resulting in a distinct and powerful light compared to ordinary sources. Laser waves are commonly employed in the exploration of diffraction and interference. Modeling the production of laser waves involves simulating the diffraction of light waves through a 1.2 mm diameter circular hole. Are laser beams truly parallel, demonstrating zero spreading? Justify your answer

Laser light of wavelength 650 nm is emitted from a tube with a radius of 0.60 mm. The emission can be modeled as diffraction from a circular hole of a radius of 0.60 mm, according to wave optics. Find the radius of the laser beam when it has covered 4.0 m from the point of emission. The wave model applies because the wave spreads significantly at 4.0 m compared to the size of the emission opening.

A satellite dish of diameter 2.50 m used in internet communication emits waves at 11.75 GHz. The dish is modeled like a circular aperture where the waves diffract. Suppose the dish radiates power at 3.0 kW; find the average wave intensity at 12 km.

A monochromatic beam of light with a wavelength of λ is incident on a single slit. The width of the slit is 150λ. The diffraction pattern is observed on a screen placed 3.25 m away from the slit. Calculate the width of the central maximum in the resulting diffraction pattern.

In an experimental setup, a beam of light from an argon-ion laser with a wavelength of λ = 488 nm is directed through a narrow slit of width 0.23 mm. The graph of the intensity of the resulting diffraction pattern on the screen is shown below. Calculate the distance between the screen and the slit.

A coherent beam of light of wavelength 630 nm is directed toward a single slit. The diffraction pattern observed on a screen positioned at a distance D behind the slit displays a central maximum with a width of 1.8 cm. Determine the wavelength of light that would produce a central maximum with a width of 2.7 cm on a screen positioned at a distance of 1.9D behind the same slit.

A single slit diffraction pattern is observed on a screen placed at a distance d behind a 375 μm narrow slit. The light used has a wavelength of 560 nm. The observed intensity pattern is shown in the figure below. Determine the distance d.

Monochromatic light of wavelength 678 nm falls on a narrow slit and then passes through a lens with a focal length of 70.0 cm. Determine the slit width if the distance between the first-order minima from the center of the screen is 7.55 mm.

Light rays are falling on a narrow slit. 

(i) Without finding all the angles, determine the total number of dark fringes formed on a screen (total for both sides of the central bright spot). Consider slit width as 0.0578 mm and wavelength of light as 570 nm. 

(ii) Calculate the angle for the dark fringe that will occur halfway from the central maximum.

A teacher is playing a 5.0 cm wavelength constant tone sound through a speaker. The sound wave passes through a 10 cm hole in the wall to the next room, where it is intercepted by a sound level meter placed at a distance of 3.0 m from the wall. The sound level meter is moved along a perpendicular line from I, the point that is aligned with the center of the hole, toward the ceiling. Determine the distances from I at which the wave intensity is zero.

In a water park, surface waves are generated in a large swimming pool and propagate at a speed of 0.2 m/s. A 5.0 m wall stands in the pool perpendicular to the direction of propagation of the waves and has an opening in its center. Using a wave profile device, you measure that every 30 seconds, 45 wave crests strike the wall. You also notice that no waves reach the opposite side of the swimming pool, 4.0 m away from the wall, at a position of 0.40 m from the point directly opposite the opening. However, waves do reach the opposite side everywhere within this distance. Determine the width of the wall opening.

An oscillator in a water wave tank generates plane waves at a frequency of 2.5 Hz. The waves propagate at a speed of 4.0 cm/s. The waves strike at normal incidence, the gap between two long rods fixed to the wall of the tank. At 20 cm from the rods, a diffraction pattern is produced. The first diffraction minimum is 3.5 cm from the central maximum. Find the diffraction angle θ for the second and third diffraction minimums.

Two half-razor blades are placed side by side, with a narrow space between them, to form a single slit of width a. A monochromatic beam of wavelength 0.520 μm passes through the slit. On a board placed very far from the blades, a Fraunhofer diffraction pattern is observed. The first dark fringe is visible at θ=±π/2 rad. i) Determine the width of the formed slit and ii) the ratio of the intensity observed at θ=π/6 to the intensity of the central bright fringe I₀.

A monochromatic light beam with a wavelength of 457 nm strikes a narrow single slit with a width of 150 μm. A diffraction pattern is formed on a paper graph 2.0 m away from the slit. The central maximum has an intensity of I₀. What would be the distance measured between the central maximum and the first dark fringe on the paper graph?

A helium-neon laser beam of wavelength 632.8 nm is directed to a vertical slit of width 350 μm. The diffraction pattern composed of bright and dark fringes is viewed on a board at 2.00 m from the slit. The bright central fringe occurs at θ=0°. A Photosensor moves across the viewing board measuring the intensity of the diffracted light as a function of the horizontal distance. An intensity of 4.25 ×10 ^-6 W/m ² is measured at θ=0°. The detector is moved to point P. Point P is located three-quarters of the distance between the bright central fringe and the first dark fringe, beginning from the bright central fringe. Determine the measured intensity at point P.

A long narrow aperture of width 200 μm is used to diffract monochromatic plane waves of wavelength 514 nm. A diffraction pattern is observed on a screen parallel to the slit and 4.00 m from it. The maximum intensity at the central bright fringe is 1.25 × 10^-6 W/m². Determine the expected intensity on the screen where the angle of diffraction θ is 1.5°.

A monochromatic laser shines through a single slit of width 56.0 μm. The resultant diffraction pattern is analyzed at a distance d from the slit using a photocell detector and computer software. At a point 3.00° away from the central bright fringe, the total phase difference between the wave received from the top and the wave received from the bottom of the slit is 34.0 rad. Determine the laser wavelength.

A collimated monochromatic beam of light is incident on an aperture of width 425 μm. The intensity distribution of light as a function of the diffraction angle θ relative to the original direction of the beam is measured with a light sensor. The central bright fringe has an intensity of 7.00 ×10^-6 W/m². At an angle θ of 1.15 °, the phase difference between the rays from the top and bottom of the slit is 110 rad. Calculate the intensity of light diffracted at θ = 1.15 °.

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?

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 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.

Hydrogen ions, H⁺ (also called protons), are accelerated through a potential difference of 310 V. The protons pass through a circular hole of radius 25 nm. Calculate the radius of the circular spot made by the ions when they strike a screen located 1.8 m from the circular hole. m_p = 1.673 × 10^-27 kg, q_p = +e = 1.60218 × 10^-19 C.

A circular hole of radius R is illuminated with the light of wavelength 700 nm. The central maxima formed by light passing through the hole has a radius of 0.4R when the screen is located at a distance of 60 cm measured from the circular hole. Find the value of R, expressed in mm.