You have a telescope that consists of two converging lenses which are placed a distance apart which is approximately equal to the sum of their focal lengths. Focal length 1 is approximately 5.5cm and focal length 2 is approximately 25cm. The lens closest to the object should have a reasonably long focal length and the eyepiece lens should have a relatively short focal length to get good magnification.

a. draw a scale ray diagram for a telescope using one long and one short focal length lens.

b. Estimate how much larger your distance object appears through your telescope and then calculate the angular magnification.

Question

High School

Answer :

BurtonLuke BurtonLuke · Answer 1 · 2023-11-06T18:59:31-05:00

b) Therefore, the object viewed through the telescope appears 0.22 times smaller than its actual size.

a) The ray diagram of the telescope using one long and one short focal length lens is shown in the figure below:

b) The formula to calculate angular magnification is given by the equation below:

Angular Magnification = (Angle subtended by the image) / (Angle subtended by the object)

Here, The distance between the two lenses,

d = f1 + f2 = 5.5 + 25 = 30.5 cm.

The magnification produced by the objective lens M1 is given by the equation below:

M1 = -f1 / d = -5.5 / 30.5 = -0.18

The magnification produced by the eyepiece lens M2 is given by the equation below:

M2 = d / f2 = 30.5 / 25 = 1.22

The total magnification is the product of the individual magnifications.

Therefore, the total magnification of the telescope is given by the equation below:

M = M1 x M2

M = -0.18 x 1.22

M = -0.22

The negative sign indicates that the image is inverted, which is common in telescopes.

The angular magnification of the telescope is given by the equation below:

Angular Magnification = (Angle subtended by the image) / (Angle subtended by the object)

Angular Magnification = (-0.22) / 1

Angular Magnification = -0.22

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