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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°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 85πrad.

Step by step solution

01

Identification of given data

The wavelength of the light is λ=589nm.

The angle of diffraction minima from center of slit is θ=30°.

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:

Δx=d2sinθ

Substitute all the values in equation.

Δx=0.10mm2sin30°Δx=0.025mm

04

Determination of phase difference

The path difference of diffraction is given as:

Δϕ=2πλΔx

Substitute all the values in equation.

Δϕ=2π589nm10-9m1nm0.025mm10-3m1mmΔϕ=85πrad

Therefore, the path difference of diffraction is 85πrad.

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Most popular questions from this chapter

A grating with d = 1.50 mm is illuminated at various angles of incidence by light of wavelength 600 nm. Plot, as a function of the angle of incidence (0 to 90°), the angular deviation of the first order maximum from the incident direction.

In Fig. 36-48, an x-ray beam of wavelengths from 95.0 to 140 pm is incident at θ=45° to a family of reflecting planes with spacing d=275pm.What are the (a) longest wavelength λ and (b) associated order number m and the (c) shortestλ and (d) associated m of the intensity maxima in the diffraction of the beam?

In a single-slit diffraction experiment, what must be the ratio of the slit width to the wavelength if the second diffraction minima are to occur at an angle of 37.0° from the center of the diffraction pattern on a viewing screen?

Suppose that the central diffraction envelope of a double-slit diffraction pattern contains 11 bright fringes and the first diffraction minima eliminate (are coincident with) bright fringes. How many bright fringes lie between the first and second minima of the diffraction envelope?

A beam of light consisting of wavelengths from460.0nmto640.0nmis directed perpendicularly onto a diffraction grating with 160 lines/mm. (a) What is the lowest order that is overlapped by another order? (b) What is the highest order for which the complete wavelength range of the beam is present? In that highest order, at what angle does the light at wavelength (c)460.0nmand (d) 640.0nmappear? (e) What is the greatest angle at which the light at wavelength460.0nmappears?
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