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Chapter 36: Q88P (page 1114)

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?

Short Answer

Expert verified

The ratio of slit width and wavelength is 3.33

Step by step solution

01

Identification of given data

The given data can be listed below,

  • The angle of diffraction minima is,θ=37°
  • The order of the diffraction minima is,m=2
02

Concept/Significance of single slit diffraction

When light passes through a single, narrow slit and comes to rest on a plane at a great distance from the slit, this is known as diffraction.

03

Determination of the ratio of the slit width to the wavelength

The brags law of diffraction is given by,

asinθ=mλaλ=msinθ

Here,λ is the wavelength of the light, ais the slit width, m is the order of diffraction minima.

Substitute all the values in the above,

aλ=2sin37°=20.601=3.33

Thus, the ratio of slit width and wavelength is 3.33.

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Most popular questions from this chapter

(a) A circular diaphragm 60 cm in diameter oscillates at a frequency of 25 kHz as an underwater source of sound used for submarine detection. Far from the source, the sound intensity is distributed as the diffraction pattern of a circular hole whose diameter equals that of the diaphragm. Take the speed of sound in water to be 1450 m/s and find the angle between the normal to the diaphragm and a line from the diaphragm to the first minimum. (b) Is there such a minimum for a source having an (audible) frequency of 1.0 kHz?

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

Monochromatic light (wavelength=450nm) is incident perpendicularly on a single slit (width=0.4mm). A screen is placed parallel to the slit plane, and on it the distance between the two minima on either side of the central maximum is 1.8mm.

(a) What is the distance from the slit to the screen? (Hint:The angle to either minimum is small enough thatsinθ≈tanθ.)

(b) What is the distance on the screen between the first minimum and the third minimum on the same side of the central maximum?

In June 1985, a laser beam was sent out from the Air Force Optical Station on Maui, Hawaii, and reflected back from the shuttle Discovery as it sped by 354 km overhead. The diameter of the central maximum of the beam at the shuttle position was said to be 9.1 m, and the beam wavelength was 500 nm. What is the effective diameter of the laser aperture at the Maui ground station? (Hint: A laser beam spreads only because of diffraction; assume a circular exit aperture.)

Babinet’s principle. A monochromatic bean of parallel light is incident on a “collimating” hole of diameter x≫λ . Point P lies in the geometrical shadow region on a distant screen (Fig. 36-39a). Two diffracting objects, shown in Fig.36-39b, are placed in turn over the collimating hole. Object A is an opaque circle with a hole in it, and B is the “photographic negative” of A . Using superposition concepts, show that the intensity at P is identical for the two diffracting objects A and B .
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