Question

A refracting telescope has an objective lens with a focal length of $2.20 \mathrm{m}\( and an eyepiece with a focal length of \)1.5 \mathrm{cm} .$ If you look through this telescope the wrong way, that is, with your eye placed at the objective lens, by what factor is the angular size of an observed object reduced?

Short answer

Answer: The angular size of an observed object is reduced by a factor of approximately 0.0068.

Step-by-step solution

Write the formula for the magnification of a refracting telescope

The magnification M of a refracting telescope can be calculated using the formula: M = \frac{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.

Substitute given values into the formula

The objective lens has a focal length of \(2.20 \mathrm{m}\), and the eyepiece has a focal length of \(1.5 \mathrm{cm}\). To be consistent with units, we will convert the focal length of the eyepiece to meters: \(f_e = 1.5 \mathrm{cm} * \frac{1 \mathrm{m}}{100 \mathrm{cm}} = 0.015 \mathrm{m}\). Now, we can substitute these values into the magnification formula: M = \frac{2.20 \mathrm{m}}{0.015 \mathrm{m}}

Calculate the magnification

Now, we can calculate the magnification of the refracting telescope when used in the incorrect manner: M = \frac{2.20}{0.015} = 146.67

Determine the angular size reduction factor

The magnification of the telescope when used correctly is 146.67. However, since the telescope is being used incorrectly, the magnification is inverted (i.e., 1/M). Therefore, the angular size reduction factor is: Angular size reduction factor = \frac{1}{M} = \frac{1}{146.67} \approx 0.0068 So, when looking through this telescope the wrong way, the angular size of an observed object is reduced by a factor of approximately 0.0068.