When an x-ray beam is scattered off the planes of a crystal, the scattered beam creates an interference pattern. This phenomenon is called Bragg scattering. For an observer to measure an interference maximum, two conditions have to be satisfied: 1. The angle of incidence has to be equal to the angle of reflection. 2. The difference in the beam's path from a source to an observer for neighboring planes has to be equal to an integer multiple of the wavelength; that is, 2d sin(0) = mx for m=1,2,.... The path difference 2d sin(0) can be determined from the diagram ( Figure 1). The second condition is known as the Bragg condition. ▾ ▼ Part A An x-ray beam with wavelength 0.250 nm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 21.0°. What is the spacing d between the planes of the crystal? Express your answer in nanometers to four significant figures. VT| ΑΣΦ/ 3 d- 0.1339 M ? Submit Previous Answers Request Answer Part B X Incorrect; Try Again; 4 attempts remaining nm Find the angle 82 at which you will find a second maximum. Express your answer in degrees to three significant figures.

Monochromatic light of wavelength 461 nm from a distant source passes through a slit that is 0.0310 mm wide. In the resulting diffraction pattern, the intensity at the center of the central maximum (θ = 0o) is 1.00×10−4 W/m^2. What is the intensity at a point on the screen that corresponds to θ = 1.20o?

The figure shows four different cases where light of wavelength A reflects from both the top and the bottom of a thin film of thickness d. The indices of refraction of the film and the media above and below it are indicated in the figure(Figure 1). Figure 1.6 1 1.5 1.4 1.4 1.5 1.6 1.5 1.6 1.4 2 3 1 of 1 4 1.4 1.6 1.5 Y Part A For which of the cases will the two reflected rays undergo constructive interference if d=X/4? constructive interference occurs in case 2 and case 3 O constructive interference occurs in case 2 and case 4 constructive interference occurs in case 3 and case 4 constructive interference occurs in case 1 and case 2 Submit Part B Request Answer For which of the cases will the two reflected rays undergo constructive interference if d=λ/2? O constructive interference occurs in case 2 and case 3 O constructive interference occurs in case 2 and case 4 O constructive interference occurs in case 3 and case 4 constructive interference occurs in case 1 and case 2

You measure three segments of the distance between a diffraction slit an the screen on which the pattern forms: x1 = (15.8 ± 0.2) cm, x2 = (6.7 ± 0.1) cm, and x3 = (11.3 ± 0.1). What is the uncertainty of the total distance x1 + x2 + x3? Group of answer choices 0.4 cm 0.5 cm 0.2 cm 0.3 cm 0.1 cm

The pupil of an eagle's eye has a diameter of 6.0 mm. Two field mice are separated by 0.010 m. From a distance of 201 m, the eagle sees them as one unresolved object and dives toward them at a speed of 16 m/s. Assume that the eagle's eye detects light that has a wavelength of 550 nm in vacuum. How much time passes until the eagle sees the mice as separate objects? t = i

Electromagnetic Plane Waves: In infrared optical systems germanium is often used to form optical components. For infrared wavelengths, germanium can be considered lossless, non-magnetic (u- 1) and has a relative dielectric constant e 16. Consider a plane wave inside a piece of germanium incident at the interface between germanium and air. The plane wave is polarized parallel to the plane of incidence and the angle of incidence is halfway between the Brewster angle and the critical angle for total internal reflection. Germanium: Air: H1 = Ho i E1 = 16e, H2 = Ho i €2 = €o %3. Be A, a) What is the angle of incidence? b) What are the reflection and transmission coefficients for the wave at this angle of incidence?