/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 53 A slide projector has a convergi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 26: Problem 53

A slide projector has a converging lens whose focal length is 105.00 mm. (a) How far (in meters) from the lens must the screen be located if a slide is placed 108.00 mm from the lens? (b) If the slide measures 24.0 \(\mathrm{mm} \times 36.0 \mathrm{mm}\) what are the dimensions (in mm) of its image?

Short Answer

Expert verified
(a) Approximately 3.78 meters; (b) Image dimensions are approximately 735 mm x 1103 mm.

Step by step solution

01

Identify known variables

We know the focal length of the lens, \( f = 105.00 \) mm, and the object distance (distance of the slide from the lens), \( d_o = 108.00 \) mm. We need to find the image distance, \( d_i \), first.
02

Apply the lens formula

The lens formula is \( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \). Substitute the known values: \( \frac{1}{105} = \frac{1}{108} + \frac{1}{d_i} \).
03

Calculate the image distance

Rearrange the lens formula to solve for \( d_i \): \( \frac{1}{d_i} = \frac{1}{105} - \frac{1}{108} \). Evaluate this expression to find \( d_i \).
04

Convert image distance to meters

Once you find \( d_i \) in millimeters, convert that distance to meters by dividing by 1000.
05

Determine the magnification of the image

The magnification, \( m \), is given by \( m = -\frac{d_i}{d_o} \). Calculate \( m \) using the values of \( d_i \) and \( d_o \) from previous steps.
06

Find the dimensions of the image

Use the magnification to find the dimensions of the image. If the slide measures \( 24.0 \) mm \( \times \) \( 36.0 \) mm, then the image dimensions \( = m \times 24.0 \) mm by \( m \times 36.0 \) mm. Compute these values.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Lens Formula
The lens formula is a key tool in understanding how lenses work. It is fundamentally important in optical systems, such as slide projectors, to determine where an image will form. The lens formula is given by:\[ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \]
  • Where, \( f \) represents the focal length of the lens.
  • \( d_o \) is the object distance, which is how far the object (like a slide) is from the lens.
  • \( d_i \) is the image distance, the position where the image shows up behind the lens.
Using this formula allows us to predict the placement of the screen needed to catch the projected image. By knowing two of these variables, we can easily calculate the third.
Focal Length
The focal length is a central concept in optics. It measures how strongly a lens converges or diverges light. For a converging lens, like the one in a slide projector, the focal length is positive. It indicates the distance from the lens to the point where parallel rays of light converge.In our scenario with the slide projector, we have:
  • Focal length, \( f = 105.00 \) mm.
Knowing the focal length helps us determine where light from an object will focus after passing through the lens. It's the backbone of calculating image and object distances.
Magnification Calculation
Magnification tells us how much larger or smaller the image is compared to the object. For lenses, it is calculated using:\[ m = -\frac{d_i}{d_o} \]
  • Here, \( m \) is the magnification factor.
  • A negative sign indicates that the image is inverted.
By knowing the image distance \( d_i \) and object distance \( d_o \), you can find the magnification. High magnification means a larger image, crucial for projecting large images from small slides.
Image Distance
The image distance \( d_i \) is the distance between the lens and the image it forms. In optical devices, like projectors, knowing the image distance allows you to place the screen correctly.To find \( d_i \), rearrange the lens formula:\[ \frac{1}{d_i} = \frac{1}{f} - \frac{1}{d_o} \]
  • Calculate \( \frac{1}{d_i} \) first.
  • Invert the result to get \( d_i \).
Once \( d_i \) is found in millimeters, convert it to meters by dividing by 1000, if required. This transformation is essential for proper screen placement in meters.
Object Distance
Object distance \( d_o \) is the measurement from the lens to the object being projected. Here, it's crucial in calculating other variables such as image distance and magnification.In our exercise:
  • Object distance \( d_o = 108.00 \) mm for the slide.
Together with focal length and image distance, object distance helps in predicting how an image is formed and where to place the image capture surface, like a screen.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Two converging lenses \(\left(f_{1}=9.00 \mathrm{cm} \text { and } f_{2}=6.00 \mathrm{cm}\right)\) are separated by 18.0 \(\mathrm{cm}\) . The lens on the left has the longer focal length. An object stands 12.0 \(\mathrm{cm}\) to the left of the left-hand lens in the combination. (a) Locate the final image relative to the lens on the right. (b) Obtain the overall magnification. (c) Is the final image real or virtual? With respect to the original object, (d) is the final image upright or inverted and (e) is it larger or smaller?

An office copier uses a lens to place an image of a document onto a rotating drum. The copy is made from this image. (a) What kind of lens is used, converging or diverging? If the document and its copy are to have the same size, but are inverted with respect to one another, (b) how far from the document is the lens located and (c) how far from the lens is the image located? Express your answers in terms of the focal length \(f\) of the lens.

The drawing shows a rectangular block of glass \((n=1.52)\) surrounded by liquid carbon disulfide \((n=1.63) .\) A ray of light is incident on the glass at point A with a \(30.0^{\circ}\) angle of inci- dence. At what angle of refraction does the ray leave the glass at point \(\mathrm{B} ?\)

A filmmaker wants to achieve an interesting visual effect by filming a scene through a converging lens with a focal length of 50.0 m. The lens is placed between the camera and a horse, which canters toward the camera at a constant speed of 7.0 m/s. The camera starts rolling when the horse is 40.0 m from the lens. Find the average speed of the image of the horse (a) during the first 2.0 s after the camera starts rolling and (b) during the following 2.0 s.

In a certain time, light travels 6.20 km in a vacuum. During the same time, light travels only 3.40 km in a liquid. What is the refractive index of the liquid?
See all solutions

Recommended explanations on Physics Textbooks

Wave Optics

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Fluids

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Geometrical and Physical Optics

Read Explanation

Quantum Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.