Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Once dark adapter, the pupil of your eye is approximately 7mmdiameter. The headlights of an oncoming car are 120cmapart. if the lens of your eye is diffraction-limited, at what distance are the two headlights marginally resolved? assume a wavelength of 600nmand that the index of refraction inside the eye is 1.33

(Your eye is not really good enough to resolve headlight at this distance, due both to aberrations in the lens and to the size of the receptors in your retina, but it comes reasonably close.

Short Answer

Expert verified

The two headlights marginally resolved at15.30kmdistence.

Step by step solution

01

Given information

We have given that:

pupil's eye 7mmdiameter.

headlights of car 120cm.

assume wavelength 600nm.

refraction inside the eye 1.33.

Distance between oncoming carslocalid="1649144003539" x=1.2m,

diameter of eyeD=7x10-3m,

wavelength of airλair=600nm

and refractive indexn=1.33.

We need to find the value of λ.

02

Simplification

Let us find the value of λ,

λ=λair/n

substituting the value in equation,

λ=600nm1.33

λ=450nm

By using the formula we need to find the value of L,

localid="1649143988920" x=αL

where α=1.22λD

localid="1649143979018" x=1.22λDL

localid="1649143956866" 1.22λD=xL

L=11.22λD

localid="1649143936404" L=x×D1.22λ

By substituting the values in the equation we get,

L=1.20m(7.0x10-3m)1.229(450x10-9m)

L=15300.54m15.30km.

Here, Lis the distance between two headlights marginally resolved.

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.

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 2.0-cm-tall object is 20cmto the left of a lens with a focal length of10cmA second lens with a focal length of 15cmis30cmto the right of the first lens.

a. Use ray tracing to find the position and height of the image. Do this accurately using a ruler or paper with a grid, then make measurements on your diagram.

b. Calculate the image position and height. Compare with your ray-tracing answers in part a.

Yang can focus on objects 150cm away with a relaxed eye. With full accommodation, she can focus on objects 20cmaway. After her eyesight is corrected for distance vision, what will her near point be while wearing her glasses?

A diffraction-limited lens can focus light to a 10μmdiameter spot on a screen. Do the following actions make the spot diameter larger, make it smaller, or leave it unchanged?

A. Decreasing the wavelength of the light.

B. Decreasing the lens diameter.

C. Decreasing the lens focal length.

D. Decreasing the lens-to-screen distance.

A 2.0-tall object is 20cmto the left of a lens with a focal length of 10cm. A second lens with a focal length of -5cm is 30cm to the right of the first lens.

a. Use ray tracing to find the position and height of the image. Do this accurately using a ruler or paper with a grid, then make measurements on your diagram.

b. Calculate the image position and height. Compare with your ray-tracing answers in part a.

A scientist needs to focus a helium-neon laser beam (λ=633nm)to a 10-μm-diameterspot 8.0cmbehind a lens

(a) what focal-length lens should she use?

(b) what minimum diameter must the lens have?

See all solutions

Recommended explanations on Physics Textbooks

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