College Physics
College Physics
10th Edition
ISBN: 9781285737027
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
Question
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Chapter 22, Problem 42P

(a)

To determine

The critical angle for total internal reflection for light in the diamond incident on the interface between the diamond and the outside air.

(a)

Expert Solution
Check Mark

Answer to Problem 42P

The critical angle for total internal reflection for light in the diamond incident on the interface between the diamond and the outside air is 24.42° .

Explanation of Solution

Given Info: The refractive index of diamond is 2.419 .

Explanation:

Formula to calculate the critical angle is,

θc=sin1(nand)

  • θc is the critical angle
  • naand nd are the refractive index of air and diamond

Substitute 1 for na , 2.419 for nd to find θc .

θc=sin1((1)(2.419))=24.42°

Thus, the critical angle for total internal reflection for light in the diamond incident on the interface between the diamond and the outside air is 24.42° .

Conclusion:

Therefore, the critical angle for total internal reflection for light in the diamond incident on the interface between the diamond and the outside air is 24.42° .

(b)

To determine

That the light is travelling towards point P in the diamond is totally reflected.

(b)

Expert Solution
Check Mark

Answer to Problem 42P

The light is travelling towards point P in the diamond is totally reflected.

Explanation of Solution

When the light beam is travelling towards the point P, the incident angle will be 35° .

Since the incident angle is greater than the critical angle, total internal reflection will occur.

Thus, the light is travelling towards point P in the diamond is totally reflected.

Conclusion:

Therefore, the light is travelling towards point P in the diamond is totally reflected.

(c)

To determine

The critical angle at the diamond water interface.

(c)

Expert Solution
Check Mark

Answer to Problem 42P

The critical angle at the diamond water interface is 33.44° .

Explanation of Solution

Formula to calculate the critical angle at the diamond water interface is,

θc=sin1(nwnd)

  • θc is the critical angle
  • nwandnd are the refractive index of water and diamond

Substitute 1.333 for nw , 2.419 for nd , to find the value θc ,

θc=sin1(1.3332.419)=33.44°

Thus, the critical angle at the diamond water interface is 33.44° .

Conclusion:

Therefore, the critical angle at the diamond water interface is 33.44° .

(d)

To determine

The explanation when the diamond is immersed in water, does the light ray entering the top surface undergo total internal reflection.

(d)

Expert Solution
Check Mark

Answer to Problem 42P

The total internal reflection will occur.

Explanation of Solution

When the light beam is travelling towards the point P, the incident angle will be, 35° .

Since the incident angle is greater than the critical angle, total internal reflection will occur.

Thus, the total internal reflection will occur at point P.

Conclusion:

Therefore, the total internal reflection will occur at point P.

(e)

To determine

The direction of rotation of the diamond about an axis perpendicular to the page.

(e)

Expert Solution
Check Mark

Answer to Problem 42P

The direction of rotation of the diamond about an axis perpendicular to the page is clockwise.

Explanation of Solution

To have light leaved the diamond at point P, we have to diminish the edge of rate now. Along these lines, we ought to turn the diamond clockwise, along these lines conveying the typical line nearer to the occurrence beam at point P.

Thus, the direction of rotation of the diamond about an axis perpendicular to the page is clockwise.

Conclusion:

Therefore, the direction of rotation of the diamond about an axis perpendicular to the page is clockwise.

(f)

To determine

The find the angle of rotation at which light will first exit the diamond at point P.

(f)

Expert Solution
Check Mark

Answer to Problem 42P

The find the angle of rotation at which light will first exit the diamond at point P is 2.9° .

Explanation of Solution

Calculating the angle of refraction is,

θr=(3533.44)=1.6°

  • θr is the angle of refraction

Formula to calculate the angle of rotation is,

θ=sin1(ndsinθrnw)

  • θ is the angle of rotation
  • ndandnw are the refractive index of diamond and water

Substitute 2.419 for nd , 1.333 for nw , 1.6° for θr , to find the value of θ .

θ=sin1((2.419)sin(1.6)(1.333))=2.9°

Thus, the find the angle of rotation at which light will first exit the diamond at point P is 2.9° .

Conclusion:

Therefore, the find the angle of rotation at which light will first exit the diamond at point P is 2.9° .

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Consider a light ray traveling between air and a diamond cut in the shape shown in Figure P22.42. (a) Find the critical angle for total internal reflection for light in the diamond incident on the interface between the diamond and the outside air. (b) Consider the light ray incident normally on the top surface of the diamond as shown in Figure P22.42. Show that the light traveling toward point P in the diamond is totally reflected. (c) If the diamond is immersed in water, find the critical angle at the diamond−water interface. (d) When the diamond is immersed in water, does the light ray entering the top surface in Figure P22.42 undergo total internal reflection at P ? Explain. (e) If the light ray entering the diamond remains vertical as shown in Figure P22.42, which way should the diamond in the water be rotated about an axis perpendicular to the page through 0 so that light will exit the diamond at P ? (f) At what angle of rotation in part (e) will light first exit the diamond at…
Consider a light ray traveling between air and a diamond cut in the shape as shown. (a) Find the critical angle for total internal reflection for light in the diamond incident on the interface between the diamond and the outside air. (b) Consider the light ray incident normally on the top surface of the diamond as shown. Show that the light traveling toward point P in the diamond is totally reflected. What If? Suppose the diamond is immersed in water. (c) What is the critical angle at the diamond– water interface? (d) When the diamond is immersed in water, does the light ray entering the top surface as shown undergo total internal reflection at P? Explain. (e) If the light ray entering the diamond remains vertical as shown, which way should the diamond in the water be rotated about an axis perpendicular to the page through O so that light will exit the diamond at P? (f) At what angle of rotation in part (e) will light first exit the diamond at point P?
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Chapter 22 Solutions

College Physics

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