What is the angular magnification of a telescope having objective and eyepiece lenses of a focal lengths 30cm and 3cm respectively?

Analysis

The question asks for the angular magnification ($M$) of an astronomical telescope. We are given the focal length of the objective lens ($f_o$) and the focal length of the eyepiece lens ($f_e$).

Concept

For an astronomical telescope in normal adjustment (where the final image is formed at infinity), the angular magnification is defined as the ratio of the focal length of the objective lens to the focal length of the eyepiece lens.

The formula is:

Where:

• $M$ = Angular magnification
• $f_o$ = Focal length of the objective lens
• $f_e$ = Focal length of the eyepiece lens

Solution

Step 1: Identify the given values.

• $f_o = 30\text{ cm}$
• $f_e = 3\text{ cm}$

Step 2: Apply the formula.

Step 3: Calculate the result.

The angular magnification is 10. This means the telescope makes the object appear 10 times larger than it would appear to the naked eye.

Conclusion

Comparing our result to the given options: A. 60 B. 10 C. 30 D. 90

The correct option is B.

Exam Tip

When dealing with telescope problems, always remember that the objective lens is the one with the longer focal length (it gathers more light), while the eyepiece has the shorter focal length. If you ever get a value less than 1, you likely flipped the fraction—check your work to ensure the larger number is on top!