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

Suppose you are using total internal reflection to make an efficient corner reflector. If there is air outside and the incident angle is 45.0º , what must be the minimum index of refraction of the material from which the reflector is made?

Short Answer

Expert verified

As a result, the minimum refractive index of the material used to make the reflector is 1.414.

Step by step solution

01

Definition of angle of incident

At the point of incidence, a line establishes an angle with a line perpendicular to the surface.

02

Given data and formula used

  • Critical angle, θ=45°
  • Refractive index of air, n1=1
  • The expression to find the critical angle is,

sinθ=n1n2........(1)

Here,

  • θis critical angle
  • n1is the refractive index of air.
  • n2is the refractive index of the material of the reflector.
03

Finding the Minimum index of refraction of the material

Let us find the minimum index of refraction of the material.

Rearranging the equation ( 1 ),

n2=n1sinθ..........(2)

Substituting the value of n1 by 1 andθ=45° in equation ( 2 ),

n2=1sin45°=112=2=1.414

Therefore, the material utilized to build the reflector has a minimum refractive index of 1.414.

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

Ray tracing for a flat mirror shows that the image is located adistance behind the mirror equal to the distance of the object from themirror. This is stated,\({d_i} = - {d_o}\) since this is a negative image distance(it is a virtual image).

(a) What is the focal length of a flat mirror?

(b) What is its power?

Light traveling from water to a gemstone strikes the surface at an angle of 80.0º and has an angle of refraction of 15.2º.

(a) What is the speed of light in the gemstone?

(b) What is unreasonable about this result?

(c) Which assumptions are unreasonable or inconsistent?

On the Moon’s surface, lunar astronauts placed a corner reflector, off which a laser beam is periodically reflected. The distance to the Moon is calculated from the round-trip time. What percent correction is needed to account for the delay in time due to the slowing of light in Earth’s atmosphere? Assume the distance to the Moon is precisely3.84×108m, and Earth’s atmosphere (which varies in density with altitude) is equivalent to a layer 30.0 kmthick with a constant index of refraction n=1.000293.

Using the law of reflection, explain how powder takes the shine off of a person’s nose. What is the name of the optical effect?

The Ray Aspect of Light

Suppose a man stands in front of a mirror as shown in Figure 25.50. His eyes are 1.65 mabove the floor, and the top of his head is 0.13 mhigher. Find the height above the floor of the top and bottom of the smallest mirror in which he can see both the top of his head and his feet. How is this distance related to the man's height?

Image Caption

Figure 25.50A full-length mirror is one in which you can see all of yourself. It need not be as big as you, and its size is independent of your distance from it.

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