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Chapter 36: Q2Q (page 1107)

In a single-slit diffraction experiment, the top and bottom rays through the slit arrive at a certain point on the viewing screen with a path length difference of 4.0 wavelengths. In a phasor representation like those in Fig 36-7, how many overlapping circles does the chain of phasors make?

Short Answer

Expert verified

4 overlapping circles are made.

Step by step solution

01

The given data

Given that in a single-slit diffraction experiment, the top and bottom rays through the slit arrive at a certain point on the viewing screen with a path length difference of 4.0 wavelengths.

02

Concept and Formula used

The dark fringes can be located with the general equation

asinθ=mλfor m=1, 2, 3,...

a is path length difference of slit , andλ is wavelength.

03

Take path length difference to be 4λ

Using the above equation, path length difference is4λ

So role="math" localid="1663147887994" asinθ=4λ

Here, role="math" localid="1663147935739" m=4

This is a point of minimum.

A complete circle for each minima will appear.

Thus, chain of phasors will make 4 overlapping circles.

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Most popular questions from this chapter

Estimate the linear separation of two objects on Mars that can just be resolved under ideal conditions by an observer on Earth (a) using the naked eye and (b) using the 200in.(=5.1m) Mount Palomar telescope. Use the following data: distance to Mars = 8.0×107km, diameter of pupil = 5.0mm, wavelength of light 550nm.

Visible light is incident perpendicularly on a diffraction grating of 200 rulings/mm. What are the (a) longest, (b) second longest, and (c) third longest wavelengths that can be associated with an intensity maximum at θ = 30.0°?

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