A laboratory (astronomical) telescope is used to view a scale that is 306 cm from the objective, which has a focal length of 20.0 cm; the eyepiece has a focal length of 2.40 cm. Calculate the angular magnification when the telescope is adjusted for minimum eyestrain. (Note: The object is not at infinity, and so the simple expression m = fo/fe is not sufficiently accurate for this problem. Also, assume small angles, so that tan(è) è.)
To calculate the angular magnification of the telescope, you can use the formula:
M = -(L/fe) * (1 + L/fo)
Where:
M - Angular magnification
L - Distance of the object from the objective lens
fe - Focal length of the eyepiece
fo - Focal length of the objective lens
Given:
L = 306 cm
fe = 2.40 cm
fo = 20.0 cm
Let's plug in the values and calculate the angular magnification:
M = -(306/2.40) * (1 + 306/20.0)
M = -(127.5) * (1 + 15.3)
M = -(127.5) * (16.3)
Therefore, the angular magnification when the telescope is adjusted for minimum eyestrain is approximately -2080.
Note: The negative sign indicates that the image is inverted.