Question

An observer looks at a tree of height 15 m with a telescope of magnifying power 10. To him the tree appears

• A. 10 times taller
• B. 15 times taller
• C. 10 times nearer
• D. 15 times nearer

Hint:

Magnifying power of telescope: \(M = \frac{f_o}{f_e}\). Angular magnification = \(\frac{\beta}{\alpha}\).

Answer 1

The Correct Option is C

To determine how the tree appears to the observer using a telescope with a magnifying power, we need to understand the concept of magnification in optical devices.

The magnifying power (or angular magnification) of an optical device is the factor by which the apparent size or the angle under which the object is seen is increased. In this case, the telescope has a magnifying power of 10. This means:

• The object looks 10 times larger in angular size, which also translates to appearing 10 times closer to the observer compared to the naked eye view.

However, note that the physical size of the tree doesn't change; it's an apparent change due to the optics. Hence, the logical reasoning to find the right option is based on this principle:

1. 10 times taller: This implies a linear magnification, which telescopes do not provide. They only increase angular size.
2. 15 times taller: Similar to the first option, this implies a change in the actual height, which does not occur.
3. 10 times nearer: Correct, as the telescope makes it appear 10 times closer to the observer due to the angular magnification.
4. 15 times nearer: This does not match the given magnifying power of the telescope, which is 10.

Therefore, the correct answer is that the tree appears 10 times nearer.