Q43P A movie camera with a (single) l... [FREE SOLUTION]

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Chapter 34: Q43P (page 1040)

A movie camera with a (single) lens of focal length $75 mm$ takesa picture ofa person standing $27 m$ away. If the person is $180 cm$ tall, what is the height of the image on the film?

Short Answer

Expert verified

The height of the image on the film is $0.5 cm$ .

Step by step solution

Listing the given quantities

Focal length

$f = 75 mm = 7.5 cm$

Object distance

$p = 27 m = 2700 cm$

Height of the person $H = 180 cm$

Understanding the concepts of optics

The focal length and the object distance is given in the problem. By using the lens equation, we can find the image distance. Using the relation between the magnification, the image distance and the object distance, we can find the magnification. Using the height of the object given in the problem, we can find the height of the image.

Formula:

$\frac{1}{f} = \frac{1}{i} + \frac{1}{p} m = - \frac{i}{p} m = \frac{Image height (h')}{Original height (H)}$

Calculations of the height of the image on the film

We have,

$\frac{1}{f} = \frac{1}{i} + \frac{1}{p}$

Rearranging for,

$\frac{1}{i} = \frac{1}{f} - \frac{1}{p} i = \frac{1}{\frac{1}{f} - \frac{1}{p}} = \frac{1}{\frac{1}{7.5} - \frac{1}{2700}} = 7.5 cm$

We have,

$m = - \frac{i}{p} m = \frac{Image height (h')}{Original height (H)} - \frac{i}{p} = \frac{Image height (h')}{Original height (H)}$

$\begin{array}{rcl} Image height (h') & = & - \frac{i}{p} 脳 Original height (H) \\ = & - \frac{7.5}{2700} 脳 180 \\ = & 0.5 cm \end{array}$

The height of the image on the film is $= 0.5 cm$ .

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91影视

A movie camera with a (single) lens of focal length $75 mm$ takesa picture ofa person standing $27 m$ away. If the person is $180 cm$ tall, what is the height of the image on the film?

Short Answer

Step by step solution

Listing the given quantities

Understanding the concepts of optics

Calculations of the height of the image on the film

One App. One Place for Learning.

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Study anywhere. Anytime. Across all devices.

91影视

A movie camera with a (single) lens of focal length 75mmtakesa picture ofa person standing 27maway. If the person is180cmtall, what is the height of the image on the film?

Short Answer

Step by step solution

Listing the given quantities

Understanding the concepts of optics

Calculations of the height of the image on the film

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Turning Points in Physics

Classical Mechanics

Linear Momentum

Medical Physics

Famous Physicists

Fundamentals of Physics

Study anywhere. Anytime. Across all devices.

A movie camera with a (single) lens of focal length $75 mm$ takesa picture ofa person standing $27 m$ away. If the person is $180 cm$ tall, what is the height of the image on the film?