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Chapter 36: Q11P (page 1109)

A 0.10mmwide slit is illuminated by light of wavelength 589nm. Consider a point P on a viewing screen on which the diffraction pattern of the slit is viewed; the point is at 30掳from the central axis of the slit. What is the phase difference between the Huygens wavelets arriving at point P from the top and midpoint of the slit? (Hint: See Eq. 36-4.)

Short Answer

Expert verified

The path difference of diffraction is 85蟺rad.

Step by step solution

01

Identification of given data

The wavelength of the light is 位=589nm.

The angle of diffraction minima from center of slit is 胃=30掳.

The width of slit is d=0.10mm.

02

Concept used

The angle of the diffraction is defined as the angle of central axis from the diffraction minima of different orders.

03

Determination of path difference

The path difference of diffraction is given as:

螖x=d2sin胃

Substitute all the values in equation.

螖x=0.10mm2sin30掳螖x=0.025mm

04

Determination of phase difference

The path difference of diffraction is given as:

螖蠒=2蟺位螖x

Substitute all the values in equation.

螖蠒=2蟺589nm10-9m1nm0.025mm10-3m1mm螖蠒=85蟺rad

Therefore, the path difference of diffraction is 85蟺rad.

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Most popular questions from this chapter

A diffraction grating 20.0 mm wide has 6000 rulings. Light of wavelength 589 nm is incident perpendicularly on the grating. What are the

(a) largest,

(b) second largest,

(c) third largest values of 胃at which maxima appear on a distant viewing screen?

Aslit 1.00mmwide is illuminated by light of wavelength 589nm. We see a diffraction pattern on a screen 3.00maway. What is the distance between the first two diffraction minima on the same side of the central diffraction maximum?

A spy satellite orbiting at 160 km above Earth鈥檚 surface has a lens with a focal length of 3.6 m and can resolve objects on the ground as small as 30 cm. For example, it can easily measure the size of an aircraft鈥檚 air intake port. What is the effective diameter of the lens as determined by diffraction consideration alone? Assume 位=550nm.

If, in a two-slit interference pattern, there are8bright fringes within the first side peak of the diffraction envelope and diffraction minima coincide with two-slit interference maxima, then what is the ratio of slit separation to slit width?

In the single-slit diffraction experiment of Fig.36-4,let the wavelength of the light be 500nm, the slit width be localid="1664272054434" 6渭尘, and the viewing screen be at distance localid="1664272062951" D=3.00m. Let y axis extend upward along the viewing screen, with its origin at the center of the diffraction pattern. Also let Iprepresent the intensity of the diffracted light at point P at y=15.0cm. (a) What is the ratio of Ipto the intensity Im at the center of the pattern? (b) Determine where point P is in the diffraction pattern by giving the maximum and minimum between which it lies, or the two minima between which it lies.
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