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Chapter 16: Problem 2256

An observer look at a tree of height 10 meters away with a telescope of magnifying power \(10 .\) To him, the tree appears (A) 10 times taller (B) 10 times smaller (C) 10 times nearer (D) 20 times nearer

Short Answer

Expert verified
When an observer looks at a 10-meter tall tree through a telescope with a magnifying power of \(10\), the tree appears \(10\) times taller (option A), as magnification only affects the perceived height and not the distance between the observer and the tree.

Step by step solution

01

Understand the telescope's magnifying power

The magnifying power of a telescope refers to how much larger the image of an object appears when viewed through the telescope compared to our naked eye. In this case, the telescope has a magnifying power of 10, which means that the image of the tree will appear ten times larger than if we were looking at it with the naked eye.
02

Analyze the effect on the tree's height

Since the telescope magnifies the image of the tree, making it appear 10 times larger than with the naked eye, the tree height will also appear 10 times larger when viewed through the telescope.
03

Analyze the effect of the telescope on the tree's distance

Magnifying power does not affect the distance between the observer and the object (in this case, the tree). So the distance remains the same when viewing the tree with or without the telescope.
04

Choose the correct option among the given choices

Based on the analysis in the previous steps, we established that: 1. The tree appears 10 times larger (in height) to the observer, so option (A) is correct. 2. The telescope does not affect the distance between the observer and the tree, so options (C) and (D) are incorrect. 3. The tree does not appear smaller, so option (B) is incorrect. So the correct answer is: (A) 10 times taller.

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