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 as

We first recall the basic definition of magnifying power (angular magnification) of an astronomical or terrestrial telescope. For an object placed very far away, the telescope forms an image such that the angle subtended by that image at the eye is larger than the angle subtended by the actual object when viewed with the naked eye.

If $$\alpha$$ is the small angle subtended by the object at the unaided eye and $$\beta$$ is the (larger) angle subtended by the final image of the telescope at the eye, then, by definition, the magnifying power $$M$$ of the telescope is

$$M \;=\; \frac{\beta}{\alpha}.$$

In the present problem the telescope has a magnifying power of $$M = 20$$. Hence

$$\beta = M\,\alpha = 20\,\alpha.$$

Let the real height of the tree be $$h = 10\ \text{m}$$ and let its actual distance from the observer be $$D$$ (the statement “distant tree” only tells us that $$D \gg h$$, so the small‐angle approximation is valid). Without the telescope, the angle subtended at the eye is approximately

$$\alpha \approx \tan \alpha = \frac{h}{D}.$$

After looking through the telescope the eye sees an image that subtends the larger angle $$\beta$$. If the same angle $$\beta$$ were to be produced by the real tree when viewed with the naked eye, the tree would have to be brought to some smaller distance $$D'$$ such that

$$\beta = \tan \beta \approx \frac{h}{D'}.$$

But from the magnification relation above we have $$\beta = 20\alpha$$, so

$$\frac{h}{D'} = 20 \left(\frac{h}{D}\right).$$

Cancelling $$h$$ from both sides gives

$$\frac{1}{D'} = \frac{20}{D} \quad\Longrightarrow\quad D' = \frac{D}{20}.$$

This shows that, to the observer, the telescope makes the distant tree appear to be at a distance that is $$\tfrac{1}{20}$$ of its actual distance. In ordinary language the tree seems “20 times nearer.” Its apparent height does not change; only the angle under which it is seen becomes larger.

Hence, the correct answer is Option B.