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Chapter 33: Problem 10

What would you expect to happen to the magnitude of the power of a lens when it is placed in water \((n=1.33) ?\) a) It would increase. d) It would depend if the b) It would decrease. lens was converging or c) It would stay the same. diverging.

Short Answer

Expert verified
Answer: It would decrease.

Step by step solution

01

Recall the Lensmaker's Equation

The Lensmaker's Equation relates the focal length (f) of a lens to its refractive indices (n_l and n_m) and its radii of curvature (R_1 and R_2), with n_m being the index of the surrounding medium: \( f = \frac{n_l - n_m}{(n_l/R_1) - (n_m/R_2)} \)
02

Determine the power of a lens

The power (P) of a lens is the inverse of its focal length (f): \( P = \frac{1}{f} \)
03

Analyze how the surrounding medium affects the focal length

From the Lensmaker's Equation, we can see that when the refractive index of the surrounding medium (n_m) increases, the difference (n_l - n_m) decreases, causing the focal length (f) to increase.
04

Determine how the focal length affects the power of the lens

When the focal length (f) increases, the power (P) of the lens, according to the power equation, decreases: \( P = \frac{1}{f} \) Therefore, the magnitude of the power of the lens would decrease when placed in water.
05

Choose the correct answer

Based on our analysis in the previous steps, we can now choose the correct option among a), b), c), and d). The correct answer is: b) It would decrease.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Lensmaker's Equation
Understanding the Lensmaker's Equation is essential for analyzing how lenses focus light. This equation is a formula used to calculate the focal length of a lens in air, given its shape and the refractive index of the material from which the lens is made. Mathematically expressed as:

\[ f = \frac{n_l - n_m}{\left(\frac{n_l}{R_1}\right) - \left(\frac{n_m}{R_2}\right)} \]

Here, \( f \) is the focal length of the lens, \( n_l \) is the refractive index of the lens material, and \( n_m \) is the refractive index of the medium surrounding the lens. \( R_1 \) and \( R_2 \) represent the radii of curvature of the lens's two surfaces. When a lens is placed in a different medium, such as water, the refractive index of the surrounding medium \( n_m \) changes, impacting the focal length calculated by this equation.
  • Lens shape and material dictate its focusing ability.
  • Changing the medium modifies the lens' focal length.
Refractive Index
The refractive index, symbolized as \( n \), is a dimensionless number that describes how fast light travels through a material. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the given material. The higher the refractive index, the more the light is slowed down and bent, or refracted, when entering the material.

This property not only affects how lenses bend light to focus or diverge it but also determines how much the light bends when moving from one medium to another. It's crucial when considering how lenses will behave when submerged in different mediums with varying refractive indices. For example, water has a refractive index of approximately \( 1.33 \), which causes light to slow down and bend differently compared to air, which has a refractive index of approximately \( 1 \). This change affects the power of lenses, as shown in the Lensmaker's Equation.
  • Higher refractive index means greater bending of light.
  • Each material's unique

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Most popular questions from this chapter

Which one of the following is not a characteristic of a simple two-lens astronomical refracting telescope? a) The final image is virtual. b) The objective forms a virtual image. c) The final image is inverted.

Will the magnification produced by a simple magnifier increase, decrease, or stay the same when the object and the lens are both moved from air into water?

When performing optical spectroscopy (for example, photoluminescence or Raman spectroscopy), a laser beam is focused on the sample to be investigated by means of a lens having a focal distance \(f\). Assume that the laser beam exits a pupil \(D_{o}\) in diameter that is located at a distance \(d_{\mathrm{o}}\) from the focusing lens. For the case when the image of the exit pupil forms on the sample, calculate a) at what distance \(d_{\mathrm{i}}\) from the lens is the sample located and b) the diameter \(D_{i}\) of the laser spot (image of the exit pupil) on the sample. c) What are the numerical results for: \(f=10.0 \mathrm{~cm},\) \(D_{o}=2.00 \mathrm{~mm}, d_{\mathrm{o}}=1.50 \mathrm{~m} ?\)

A converging lens will be used as a magnifying glass. In order for this to work, the object must be placed at a distance a) \(d_{\mathrm{o}}>f\). c) \(d_{\mathrm{o}}

An object of height \(h\) is placed at a distance \(d_{0}\) on the left side of a converging lens of focal length \(f\left(f
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