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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 single slit is illuminated by light of wavelengths 位a and 位b, chosen so that the first diffraction minimum of the 位acomponent coincides with the second minimum of the 位bcomponent. (a) If 位b=350nm , what is 位a? For what order number mb (if any) does a minimum of the 位b component coincide with the minimum of the 位a component in the order number (b) role="math" localid="1663142824281" ma=2 and (c) ma=3?

In Fig. 36-47, first-order reflection from the reflection planes shown occurs when an x-ray beam of wavelength0.260nmmakes an angle胃=63.8掳 with the top face of the crystal. What is the unit cell sizea0?

Consider a two-dimensional square crystal structure, such as one side of the structure shown in Fig. 36-28a.The largest interplanar spacing of reflecting planes is the unit cell size ao. Calculate and sketch the (a) second largest, (b) third largest, (c) fourth largest, (d) fifth largest, and (e) sixth largest interplanar spacing. (f) Show that your results in (a) through (e) are consistent with the general formula

d=aoh2+k2

where h and k are relatively prime integers (they have no common factor other than unity).

The radar system of a navy cruiser transmits at a wavelength of 1.6 cm, from a circular antenna with a diameter of 2.3 m. At a range of 6.2 km, what is the smallest distance that two speedboats can be from each other and still be resolved as two separate objects by the radar system?

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?
See all solutions

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