Chapter 25: Q15PE (page 930)

Suppose Figure 25.54represents a ray of light going from air through crown glass into water, such as going into a fish tank. Calculate the amount the ray is displaced by the glass $(∆ x)$ , given that the incident angle is $40 . 0^{°}$ and the glass is1.00 cmthick.

Short Answer

Expert verified

The amount of rays displayed by the glass is obtained as: 3.73 mm.

Step by step solution

Define Geometric Optics

Geometrical optics, often known as ray optics, is an optics model that describes light propagation using rays. In geometric optics, a ray is an abstraction that can be used to approximate the routes along which light propagates under particular conditions.

Evaluating the amount of rays displayed

Using Snell's law: $n_{i} \sin θ_{i} = n_{f} \sin θ_{f}$ , it is along with trigonometry that is applied in the figure below, we can find that by using $\tan θ_{1} = \frac{x_{2}}{d}$ , and $\tan θ_{2} = \frac{x_{1}}{d}$ . Besides: $∆ x = x_{2} - x_{1}$ .

The diagram is represented as:

The equation is then evaluated as:

$θ_{2} = \sin^{- 1} (\frac{n_{1} \sin θ_{1}}{n_{2}}) = \sin^{- 1} (\frac{1.00 \times \sin 40 . 0^{°}}{1.52}) = 25 . 0^{°} ∵ \tan θ_{2} = \frac{x_{1}}{d} ∴ x_{1} = d \times \tan θ_{2} ∵ \tan θ_{1} = \frac{x_{2}}{d} ∴ x_{2} = d \times \tan θ_{1}$

$∆ x = x_{2} - x_{1} = d \times (\tan θ_{1} - \tan θ_{2}) = 0.01 m \times (\tan 40 . 0^{°} - \tan 25 . 0^{°}) = 3.73 \times 10^{- 3} m = 3.73 m m$

Therefore, the amount of rays displayed by the glass is: 3.73mm.

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Suppose Figure 25.54represents a ray of light going from air through crown glass into water, such as going into a fish tank. Calculate the amount the ray is displaced by the glass $(∆ x)$ , given that the incident angle is $40 . 0^{°}$ and the glass is1.00 cmthick.

Short Answer

Step by step solution

Define Geometric Optics

Evaluating the amount of rays displayed

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Suppose Figure 25.54represents a ray of light going from air through crown glass into water, such as going into a fish tank. Calculate the amount the ray is displaced by the glass (∆x), given that the incident angle is40.0°and the glass is1.00 cmthick.

Short Answer

Step by step solution

Define Geometric Optics

Evaluating the amount of rays displayed

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Atoms and Radioactivity

Electricity

Medical Physics

Thermodynamics

Solid State Physics

Space Physics

Study anywhere. Anytime. Across all devices.

Suppose Figure 25.54represents a ray of light going from air through crown glass into water, such as going into a fish tank. Calculate the amount the ray is displaced by the glass $(∆ x)$ , given that the incident angle is $40 . 0^{°}$ and the glass is1.00 cmthick.