Ch 33: The Nature and Propagation of Light

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 33: The Nature and Propagation of Light

Problem 24b

Chapter 33, Problem 24b

A beam of light strikes a sheet of glass at an angle of 57.0° with the normal in air. You observe that red light makes an angle of 38.1° with the normal in the glass, while violet light makes a 36.7° angle. What are the speeds of red and violet light in the glass?

Verified step by step guidance

First, understand that the speed of light in a medium is related to its refractive index. The refractive index (n) can be calculated using Snell's Law, which is given by:

n = \frac{\sin (θ)}{\sin (θ')}

, where θ is the angle of incidence and θ' is the angle of refraction.

Apply Snell's Law to find the refractive index for red light. Use the given angles: θ = 57.0° and θ' = 38.1°. Substitute these values into the formula:

n = \frac{\sin (57.0)}{\sin (38.1)}

Similarly, apply Snell's Law to find the refractive index for violet light using the angles: θ = 57.0° and θ' = 36.7°. Substitute these values into the formula:

n = \frac{\sin (57.0)}{\sin (36.7)}

Once you have the refractive indices for both red and violet light, use the relationship between the speed of light in a medium and its refractive index:

v = \frac{c}{n}

, where v is the speed of light in the medium, c is the speed of light in vacuum (approximately 3.00 x 10^8 m/s), and n is the refractive index.

Calculate the speed of red light in the glass using its refractive index, and similarly calculate the speed of violet light using its refractive index. Substitute the values of c and n into the formula for each case to find the respective speeds.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Snell's Law

Snell's Law describes how light bends when it passes from one medium to another. It is expressed as n1 * sin(θ1) = n2 * sin(θ2), where n1 and n2 are the refractive indices of the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively. This law is crucial for determining the angles of light in different media.

Refractive Index

The refractive index of a medium quantifies how much light slows down when entering the medium compared to its speed in a vacuum. It is defined as n = c/v, where c is the speed of light in a vacuum and v is the speed of light in the medium. Different wavelengths of light, such as red and violet, have different refractive indices, affecting their speed in the glass.

Dispersion

Dispersion occurs when different wavelengths of light travel at different speeds in a medium, causing them to refract at different angles. This phenomenon is responsible for the separation of colors, as seen in prisms. In the context of the question, dispersion explains why red and violet light have different angles and speeds in the glass.

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Textbook Question

Unpolarized light with intensity I₀ is incident on two polarizing filters. The axis of the first filter makes an angle of 60.0° with the vertical, and the axis of the second filter is horizontal. What is the intensity of the light after it has passed through the second filter?

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Textbook Question

It is proposed to store 1.00 kWh = 3.60 × 10⁶ J of electrical energy in a uniform magnetic field with magnitude 0.600 T. If instead this amount of energy is to be stored in a volume (in vacuum) equivalent to a cube 40.0 cm on a side, what magnetic field is required?

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Textbook Question

A beam of unpolarized light of intensity I₀ passes through a series of ideal polarizing filters with their polarizing axes turned to various angles as shown in Fig. E33.27. If we remove the middle filter, what will be the light intensity at point C?

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Textbook Question

The indexes of refraction for violet light (λ = 400 nm) and red light (λ= 700 nm) in diamond are 2.46 and 2.41, respectively. A ray of light traveling through air strikes the diamond surface at an angle of 53.5° to the normal. Calculate the angular separation between these two colors of light in the refracted ray.

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Textbook Question

At the very end of Wagner's series of operas Ring of the Nibelung, Brünnhilde takes the golden ring from the finger of the dead Siegfried and throws it into the Rhine, where it sinks to the bottom of the river. Assuming that the ring is small enough compared to the depth of the river to be treated as a point and that the Rhine is 10.0 m deep where the ring goes in, what is the area of the largest circle at the surface of the water over which light from the ring could escape from the water?

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Textbook Question

Light of original intensity I₀ passes through two ideal polarizing filters having their polarizing axes oriented as shown in Fig. E33.28. You want to adjust the angle f so that the intensity at point P is equal to I₀/10. If the original light is unpolarized, what should Φ be?

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