Question

An observer looks at a distant tree of height \(10\) m with a telescope of magnifying power of \(20\). To the observer, the tree appears

• A. \(10\) times taller.
• B. \(10\) times nearer.
• C. \(20\) times nearer.
• D. \(20\) times taller.

Hint:

A telescope with magnifying power m makes distant objects look m times nearer, because the visual angle increases m times.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
The magnifying power of a telescope is \(m=\dfrac{\beta}{\alpha}\), the ratio of the angle subtended by the image to the angle subtended by the object at the unaided eye.

Step 2: Apply to the tree
With \(m=20\), the angle subtended by the tree becomes \(20\) times larger.

Step 3: Interpret the result
The tree of height \(10\text{ m}\) is not physically enlarged. A larger visual angle means the tree appears as if it were \(20\) times closer.

Step 4: Compare the options
So the tree appears \(20\) times nearer, option (C).

Final Answer:
The tree appears 20 times nearer. \[ \boxed{\text{(C) }\text{20 times nearer}} \]