Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 32: Problem 61

While driving at night, your eyes' irises dilate to 3.1 -mm diameter. If your vision were diffraction limited, what would be the greatest distance at which you could see as distinct the two headlights of an oncoming car, spaced \(1.5 \mathrm{m}\) apart? Take \(\lambda=550 \mathrm{nm}\)

Short Answer

Expert verified
The greatest distance at which the two headlights of an oncoming car can be seen distinctly can be calculated using the given variables and applying them in the Rayleigh's criterion for resolution, and the distance formula. After calculation, we get the distance value.

Step by step solution

01

Understanding the Problem

Here we need to find out the maximum distance at which two headlights of the car could be seen distinctly, when considering the eyes vision to be diffraction limited. The key data given: Diameter of iris (d) = 3.1 mm, Spacing between the headlights (s) = 1.5 m and Light wavelength (λ) = 550 nm.
02

Using the Formula

By definition of resolution, two images are said to be resolved if the distance is such that angular separation is greater or equal to the Rayleigh criterion. Hence, we will use the formula \(θ = 1.22*λ/d\) where \(θ\) is the angle subtended by an object at the observing point, \(λ\) is the wavelength of light, and \(d\) is the diameter of the circular aperture.
03

Conversion and Calculation

First convert the given measurements into same units. The diameter of Iris is given in mm, it needs to be converted into meters, hence d = 3.1 * \(10^{-3}\) m and \(λ\) = 550 * \(10^{-9}\) m. Now, we can substitute these values into Rayleigh criterion formula assuming the oncoming car is at limit of resolution, we have \(θ = 1.22*λ/d\). Calculate \(θ\)
04

Calculating Distance

We now calculate the distance using formula \(d = s/θ\), where s is the spacing between headlights. Substitute the calculated value of \(θ\) and s = 1.5 m into the formula to find the distance.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A Michelson interferometer uses light from glowing hydrogen at \(486.1 \mathrm{nm} .\) As you move one mirror, 530 bright fringes pass a fixed point in the viewer. How far did the mirror move?

You know that it's safe to microwave plastic containers, since their molecules don't respond significantly to 2.4 -GHz microwaves. But since you've learned about thin-film interference, you worry about enhanced microwave intensity due to multiple reflections in plastic cookware. You calculate the minimum thickness for a plastic tray with refractive index 1.3 that will cause enhanced reflection of microwaves incident normal to the plate. Are your worries assuaged?

A double-slit experiment with \(d=0.025 \mathrm{mm}\) and \(L=75 \mathrm{cm}\) uses 550 -nm light. Find the spacing between adjacent bright fringes.

A screen \(1.0 \mathrm{m}\) wide is \(2.0 \mathrm{m}\) from a pair of slits illuminated by 633 -nm laser light, with the screen's center on the centerline of the slits. Find the highest-order bright fringe that will appear on the screen if the slit spacing is (a) \(0.10 \mathrm{mm}\) and (b) \(10 \mu \mathrm{m}\)

Monochromatic light shines on a glass wedge with refractive index \(1.65,\) and enhanced reflection occurs where the wedge is \(450 \mathrm{nm}\) thick. Find all possible values for the wavelength in the visible range.
See all solutions

Recommended explanations on Physics Textbooks

Dynamics

Read Explanation

Radiation

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Physics of Motion

Read Explanation

Electromagnetism

Read Explanation

Measurements

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free