Meaning of magnifying power of a telescope

For a telescope, the magnifying power is defined as $M = \frac{\text{angle subtended at the eye by the image seen through telescope}}{\text{angle subtended at the eye by the object when seen directly}}.$

Given data

The telescope has magnifying power $M = 20.$

The actual height of the tree is $10\,\text{m}$, but this does not affect the answer directly, because telescope magnification concerns angular size, not linear enlargement.

Interpretation of telescope magnification

If an object subtends $20$ times the angle at the eye, it appears as if it were brought closer so that its angular size becomes $20$ times larger.

Since angular size for a distant object is approximately $\theta \approx \frac{h}{d},$ where $h$ is height and $d$ is distance, making the angle $20$ times larger is equivalent to reducing the distance to $\frac{d}{20}.$

So the tree appears 20 times nearer.

Checking options

• A: $20$ times taller — Incorrect. A telescope does not make the object actually appear linearly taller; it increases angular size.
• B: $20$ times nearer — Correct.
• C: $10$ times taller — Incorrect.
• D: $10$ times nearer — Incorrect.

Final answer

The tree appears: $\boxed{\text{20 times nearer}}$