What must be the ratio of the slit width to the wavelength for a single slit to have the first diffraction minimum at u = 45.0°?

A laser beam with wavelength λ = 550 nm hits a grating with n = 2250 grooves per centimeter. Part (b)  Find the sin of the angle, θ2, at which the 2nd order maximum will be observed, in terms of d and λ.  sin(θ2) =

A He-Ne gas laser which produces monochromatic light of a known wavelength = 6.35x10^-7m is used to calibrate a reflection grating in a spectroscope. The first-order diffraction line is found at an angle of 22 degrees to the incident beam. How many lines per meter are there on the grating?

Light of wavelength 585.5 nm illuminates a slit of width 0.70 mm. (a) At what distance from the slit should a screen be placed if the first minimum in the diffraction pattern is to be 0.93 mm from the central maximum? Answer in m (b) Calculate the width of the central maximum. Answer in mm

In the two-slit interference experiment in Fig. 5, the slit widths are each 12.0 mm, their separation is 24.0 mm, the wavelength is 600 nm, and the viewing screen is at a distance of 4.00 m. Let y = 70.0 cm. (a) Determine where P on the screen is in the two-slit interference pattern by giving the maximum or minimum on which it lies or the maximum and minimum between which it lies. (b) In the same way, for the diffraction that occurs, determine where point P is in the diffraction pattern. The AL shifts Incident one wave from wave the other, which determines the interference. Path length difference AL (b) (a) B Figure 5

632.8 nm) is used to calibrate a diffraction grating. If the first-order maximum occurs at 21.0°, what is the spacing between adjacent grooves in the grating? (In this problem, assume that the light is incident normally on the grating.) μm A helium-neon laser (1 =

Measuring distance with high precision is a critical goal in engineering. Numerous devices exist to perform such measurements, with many involving laser light. Shining light through a double slit can be used to measure distance if (1) both the wavelength of the light beam and the distance between slits are known and (2) the spacing between the minima and maxima appearing on the screen can be measured. But this method requires a physical measurement of distance on the object, which may not be practical. To create a laser-based measurement device that does not require placing a physical ruler on the object, a Nd:YAG laser is mounted inside a box so that the beam of the laser passes through two slits rigidly attached to the laser. Although 1064 nm is the principal wavelength of a Nd:YAG laser, the laser can be switched to numerous secondary wavelengths, including 1052 nm, 1075 nm, 1113 nm, and 1319 nm. Lo Laser Id Object The device is used to shine a beam on an object located nearby. The…

Light of wavelength 588.2 nm illuminates a slit of width 0.63 mm. (a) At what distance from the slit should a screen be placed if the first minimum in the diffraction pattern is to be 0.86 mm from the central maximum? (b) Calculate the width of the central maximum. Step 1 (a) As shown in the figure, dark bands or minima occur where sin 0 = m(2/a). For the first minimum, m = 1 and the distance from the center of the central maximum to the first minimum is y₁ = L tan 8, where L is the distance of the viewing screen from the slit. 32 sin dark = 22/a 31 sin dark = λ/a HE 0 -1 sin dark = -λ/a -2 sin dark = -22/a Viewing screen a Because is very small, we can use the approximation tan sin 0 = m(2/a). Substituting the approximation and solving for the distance to the screen, we have 6.3 x 10 m ³ m ) (₁ L = = y ₁ ( ² ) = x 10-3 m x 10-⁹ m m.

The width of the central peak in a single-slit diffraction pattern is 5.0 mm. The wavelength of the light is 600. nm, and the screen is 1.9 m from the slit. (a.) What is the width of the slit in microns? (D= ?)  (b.) What is the ratio of the intensity at 4.2mm from the center of the pattern to the intensity at the center of the pattern? (I/I0= ?)

A He-Ne gas laser which produces monochromatic light of a known wavelength ? =6.35 ? 10^−7 ? is used to calibrate a reflection grating in a spectroscope. The first-orderdiffraction line is found at an angle of 22 degrees to the incident beam. How many lines per meter are there on the grating?