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Chapter 36: Q6P (page 1109)

Monochromatic light of wavelength 441nmis incident on a narrow slit. On a screen 2.00maway, the distance between the second diffraction minimum and the central maximum is 1.50cm. (a) Calculate the angle of diffraction role="math" localid="1663145961694" 胃of the second minimum. (b) Find the width of the slit.

Short Answer

Expert verified

(a) The angle of diffraction for second order minima is 0.429掳.

(b) The width of slit is 1.18脳10-4m.

Step by step solution

01

Identification of given data

The wavelength of the monochromatic light is 位=441nm.

The distance of screen from narrow slit is D=2m.

The distance between central minima and second order minima is w=1.50cm.

The order of second minima is m=2.

02

Concept used

The diffraction is the phenomenon in which the light bends on the edges of the slit and pattern of light is formed on a screen.

03

Determination of angle of diffraction for second order minima

(a)

The angle of diffraction for second order minima is given as:

tan胃=wD

Substitute all the values in equation.

tan胃=1.50cm1m100cm2m胃=0.429掳

Therefore, the angle of diffraction for second order minima is 0.429掳.

04

Determination of width of slit

(b)

The width of slit is given as:

m位=dsin胃

Substitute all the values in equation.

2441nm=dsin0.429掳d=1.18脳10-4m

Therefore, the width of slit is 1.18脳10-4m.

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Most popular questions from this chapter

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.

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?

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.)

You are conducting a single slit diffraction experiment with a light of wavelength 位. What appears , on a distant viewing screen, at a point at which the top and bottom rays through the slit have a path length difference equal to (a) 5位and (b) 4.5位?

Figure shows a red line and a green line of the same order in the pattern produced by a diffraction grating. If we increased the number of rulings in the grating 鈥� say, by removing tape that had covered the outer half of the rulings 鈥� would (a) the half-widhts of the lines and (b) the separation of the lines increase, decrease, or remain the same? (c) Would the lines shift to the right, shift to the left, or remain in place
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