Physics for Scientists and Engineers, Technology Update (No access codes included)
Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 35, Problem 35.68AP

(a)

To determine

The maximum angle of incidence for which the phenomena of total internal reflection occurs at the left vertical surface.

(a)

Expert Solution
Check Mark

Answer to Problem 35.68AP

The total internal reflection will occur for all the values of angle of incidence and the maximum value for angle of incidence is 90° .

Explanation of Solution

Given Info: The light of wavelength 589nm is incident on the polystyrene block of refractive index n at an angle θ . The incident ray gets refracted from the horizontal surface by angle θ1 and strikes the left vertical surface at angle θ2 as shown in figure below.

The refractive index of the polystyrene is 1.49 and the refractive index of air is 1.00 .

Physics for Scientists and Engineers, Technology Update (No access codes included), Chapter 35, Problem 35.68AP , additional homework tip  1

Figure (I)

For total internal reflection from the left vertical surface the angle of incidence for the vertical surface must be greater than the critical angle.

(θ2>θc) (1)

The formula to calculate the critical angle is,

θc=sin1(n2n1) . (2)

Here,

θc is the critical angle.

n1 is the refractive index of the polystyrene.

n2 is the refractive index of the air.

Substitute 1.49 for n1 and 1.00 for n2 in the equation (2).

θc=sin1(1.001.49)=42.2°

From equation (1) the value of the angle θ2 must be greater than 42.2° .

From Figure (1) in triangle ABC the value of the angle θ1 is,

θ1=90°θ2

Substitute 42.2° for θ2 in the above equation.

θ1=90°42.2°=47.8°

Thus the value of θ1 is 47.8° .

Formula to calculate the value of θ from Snell’s law is,

nairsinθ=nsinθ1

Here,

nair is the refractive index of air.

n is the refractive index of polystyrene.

Substitute 1.00 for nair 1.49 for n and 47.8° for θ1 in the above equation.

nairsinθ=nsinθ1(1.00)sinθ=(1.49)sin(47.8°)sinθ=1.10

As the angle θ1 must be less than the 47.8° , (θ147.8°) , thus in the above equation the,

sinθ1.10 (3)

Thus any value of θ satisfy the equation (3) total internal reflection will occur at the left vertical surface, and the maximum angle will be less than 90° .

Conclusion:

Therefore, total internal reflection will occur at the left vertical surface for any angle less than 90° .

(b)

To determine

The angle of incidence if the polystyrene slab is immersed in water.

(b)

Expert Solution
Check Mark

Answer to Problem 35.68AP

The total internal reflection will occur for angle of incidence 30.3° when the polystyrene slab is immersed in water.

Explanation of Solution

Explanation

Given info:  The refractive index of water is 1.33 .

For the polystyrene slab surrounded in water the value of critical angle is,

θc=sin1(n2n1)

Substitute 1.33 for n2 and 1.49 for n1 in the above equation.

θc=sin1(1.331.49)=63.2°

The value of θ2 is 63.2° .

From figure (1) in triangle ABC the value of θ1 is,

θ1=90°θ2

Substitute 63.2° for θ2 in the above equation.

θ1=90°63.2°=26.8°

From Snell’s Law, calculate the value of the angle of incidence.

Physics for Scientists and Engineers, Technology Update (No access codes included), Chapter 35, Problem 35.68AP , additional homework tip  2  nwatersinθ=nsinθ1

Here,

nwater is the refractive index of water.

n is the refractive index of polystyrene.

Substitute 1.33 for nwater and 1.49 for n in the above equation.

nwatersinθ=nsinθ1(1.33)sinθ=1.49sin(26.8°)θ=30.3°

Thus when the polystyrene slab is immersed in water the angle of incidence is 30.3° .

Conclusion:

Therefore, the total internal reflection will occur for angle of incidence 30.3° when the polystyrene slab is immersed in water.

(c)

To determine

The angle of incidence for the phenomena of total internal reflection if the polystyrene slab is immersed in carbon disulphide.

(c)

Expert Solution
Check Mark

Answer to Problem 35.68AP

The refractive index of the carbon disulphide is more than the refractive index of the polystyrene, so the total internal refraction is not possible.

Explanation of Solution

Explanation

Given info:  The refractive index of carbon disulphide is 1.628 .

The phenomena of total internal reflection only takes place when the light ray is travelling form a higher refractive index material to a low refractive index material.

For the case where the polystyrene slab is immersed in the carbon disulphide the light ray at the interface of the left vertical wall will not undergo the total internal reflection as at the interface the light will be propagating form a lower refractive index material to a higher refractive material and for the phenomena of total internal reflection to occur the light must be travelling form higher refractive index material to a low refractive index material.

Hence, the phenomena of total internal reflection will not take place when the slab is immersed in carbon disulphide.

Conclusion:

Therefore, the phenomena of total internal reflection will not take place when the slab is immersed in carbon disulphide.

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Chapter 35 Solutions

Physics for Scientists and Engineers, Technology Update (No access codes included)

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