A telescope has an objective with a refractive power of 1.20 diopters and an eyepiece with a refractive power of 220 diopters. What is the angular magnification of the telescope?
Angular magnification
M= - F(objective)/F(eyepiece)
F(objective)=1/1.2 = 0.833
F(eyepiece) = -1/220= - 0.0045
M= 0.833/0.0045 = 185
To find the angular magnification of a telescope, we can use the formula:
M = -(fo/fe)
where M is the angular magnification, fo is the focal length of the objective lens, and fe is the focal length of the eyepiece.
First, we need to convert the refractive powers to focal lengths. The formula to convert refractive power (P) to focal length (f) is:
f = 1/P
Using this formula, we can find the focal lengths of the objective lens (fo) and the eyepiece (fe).
fo = 1 / 1.20 = 0.833 meters
fe = 1 / 220 = 0.0045 meters
Now, we can substitute the values into the formula for angular magnification:
M = -(0.833 / 0.0045)
Calculating this fraction gives us:
M = -185.11
Since angular magnification can have a negative sign, we can ignore it in this case.
Therefore, the angular magnification of the telescope is approximately 185.11.
To find the angular magnification of a telescope, you can use the formula:
M = - f/fe
Where:
M is the angular magnification,
f is the focal length of the objective lens, and
fe is the focal length of the eyepiece.
In this case, we are given the refractive power of the lenses, which is the reciprocal of the focal length in meters. The formula for refractive power is:
P = 1/f
Rearranging this equation, we have:
f = 1/P
For the objective lens, we are given that the refractive power is 1.20 diopters:
f = 1/1.20 = 0.833 meters
For the eyepiece lens, we are given that the refractive power is 220 diopters:
fe = 1/220 = 0.00455 meters
Now, we can substitute these values into the formula for angular magnification:
M = - f/fe
= - 0.833/0.00455
≈ -182.64
The negative sign indicates that the image formed by the telescope is inverted. Therefore, the angular magnification of the telescope is approximately 182.64, and the image is inverted.