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Chapter 4: Problem 56

Diffraction spreading for a flashlight is insignificant compared with other limitations in its optics, such as spherical aberrations in its mirror. To show this, calculate the minimum angular spreading of a flashlight beam that is originally \(5.00 \mathrm{cm}\) in diameter with an average wavelength of \(600 \mathrm{nm}\)

Short Answer

Expert verified
The minimum angular spreading of a flashlight beam with a diameter of 5.00 cm and an average wavelength of 600 nm is approximately \(1.20 \times 10^{-8}\) radians.

Step by step solution

01

Before using the formula for angular spreading, we need to convert the given values to meters. Diameter of the flashlight beam, \(b = 5.00\,cm = 0.0500\,m\) Wavelength of the light, \(\lambda = 600\,nm = 600 \times 10^{-9}\, m\) Now, we will use these values for \(b\) and \(\lambda\) in the formula to calculate the minimum angular spreading. #Step 2: Calculate the angular spreading using the formula#

To find the minimum angular spreading, \(\Delta \theta\), we can use the formula: \[ \Delta \theta \approx \frac{\lambda}{b} \] Substitute the values of \(\lambda\) and \(b\): \[ \Delta \theta \approx \frac{600 \times 10^{-9}\,m}{0.0500\,m} \] Now, divide the values and find the answer: \[ \Delta \theta \approx 1.20 \times 10^{-8} \, rad \] So, the minimum angular spreading of the flashlight beam is approximately \(1.20 \times 10^{-8}\) radians.

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Most popular questions from this chapter

Shown below is the central part of the interference pattern for a pure wavelength of red light projected onto a double slit. The pattern is actually a combination of singleand double-slit interference. Note that the bright spots are evenly spaced. Is this a double-or single-slit characteristic? Note that some of the bright spots are dim on either side of the center. Is this a single-or double-slit characteristic? Which is smaller, the slit width or the separation between slits? Explain your responses

What is the spacing between structures in a feather that acts as a reflection grating, giving that they produce a firstorder maximum for \(525-\mathrm{nm}\) light at a \(30.0^{\circ}\) angle?

If you and a friend are on opposite sides of a hill, you can communicate with walkie-talkies but not with flashlights. Explain.

A diffraction grating produces a second maximum that is \(89.7 \mathrm{cm}\) from the central maximum on a screen \(2.0 \mathrm{m}\) away. If the grating has 600 lines per centimeter, what is the wavelength of the light that produces the diffraction pattern?

The limit to the eye's acuity is actually related to diffraction by the pupil. (a) What is the angle between two just-resolvable points of light for a 3.00 -mm-diameter pupil, assuming an average wavelength of \(550 \mathrm{nm}\) ? (b) Take your result to be the practical limit for the eye. What is the greatest possible distance a car can be from you if you can resolve its two headlights, given they are \(1.30 \mathrm{m}\) apart? (c) What is the distance between two just-resolvable points held at an arm's length (0.800 m) from your eye? (d) How does your answer to (c) compare to details you normally observe in everyday circumstances?
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