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

What is the thinnest film of a coating with n=1.42 on glass (n=1.52) for which destructive interference of the red component (650nm) of an incident white light beam in air can take place by reflection?

Short Answer

Expert verified

The thinnest film of a coating is 114nm.

Step by step solution

01

Formulas used to solve the question

Destructive interference

2t=(m+12)ฮป

Snellโ€™s law:

n1ฮป1=n2ฮป2

02

Determine the thickness in terms of ฮป

Given: nair=1.0

ncoating=1.42nglass=1.52ฮปair=650nm=650*10-9m

Light beam reflects from a surface that has a greater index of refraction than the index of refraction of the first medium, the wave experiences a phase change. This means that the first ray experiences the phase change and the second ray also experiences a phase change.

From equation (1), at m = 0 for the thinnest coating

t=14ฮป (3)

03

Determine the thickness

From equation (2),

ncoatingฮปcoating=nairฮปair

โ‡’ฮปcoating=nairฮปairncoating

Plug the given,

โ‡’ฮปcoating=ฮปairncoating

Plug into (3),

t=ฮปair4ncoating=650โˆ—10โˆ’94โˆ—1.42=114nm

Thus, the thinnest film of a coating is 114nm.

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

Study anywhere. Anytime. Across all devices.

Sign-up for free