Question

An astronomical telescope of tenfold angular magnification has a length of 44 cm. The focal length of the objective is

• A. 44 cm
• B. 440 cm
• C. 4 cm
• D. 40 cm.

Answer 1

The Correct Option is D

To determine the focal length of the objective of an astronomical telescope, we use the given parameters: the telescope has an angular magnification of tenfold (10x) and a length of 44 cm.

An astronomical telescope in its simplest form consists of two lenses: an objective lens and an eyepiece lens. The objective lens gathers light from distant objects and forms an image, while the eyepiece magnifies this image for viewing.

The length of the telescope, in normal adjustment (when the final image is at infinity), is given by the formula:

L = f_o + f_e

where f_o is the focal length of the objective lens and f_e is the focal length of the eyepiece lens.

The angular magnification (M) of an astronomical telescope is given by:

M = \frac{f_o}{f_e}

We are given:

• The angular magnification (M = 10)
• The length of the telescope (L = 44\, \text{cm})

Using the magnification formula:

f_e = \frac{f_o}{M}

Substituting this into the length formula, we get:

L = f_o + \frac{f_o}{M}

Rearranging the formula gives:

44 = f_o + \frac{f_o}{10}

Take f_o as a common factor:

44 = f_o \left(1 + \frac{1}{10}\right)

Simplify the expression:

44 = f_o \left(\frac{11}{10}\right)

Solving for f_o:

f_o = 44 \times \frac{10}{11}

f_o = 40 \, \text{cm}

Therefore, the focal length of the objective is 40 cm. The correct option is 40 cm.