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Chapter 34: Q88P (page 1042)

If the angular magnification of an astronomical telescope is 36 and the diameter of the objective is 75 mm, what is the minimum diameter of the eyepiece required to collect all the light entering the objective from a distant point source on the telescope axis?

Short Answer

Expert verified

The minimum diameter of the eyepiece is 2.1 mm.

Step by step solution

01

Step 1: Given data

  • Angular magnification= 36.
  • Diameter of the objective is,d=75mm=0.075m.
02

Determining the concept

Find the magnification in terms of the diameter of the object and the eyepiece. Using that, calculate the minimum diameter of the eyepiece.

Formulae are as follows:

Magnification for the telescope is

M=DiameterofobjectDiameteroftheeyepiece=DoDep

Here, Dois the diameter of the object and Depis the diameter of the eyepiece.

03

Determining the minimum diameter of the eyepiece required to collect all the light entering the objective from a distant point source on the telescope axis.

Let us find the magnification using the above diagram.

Let us find the ratio.

Depfey=D0fob+feyDepfey鈮�D0fobDep=D0f0bfey

Angular magnification,

localid="1663080166275" m胃=f0bfey

鈭�Dep=D0m胃

Using the given values,

Dep=0.07536=0.00208m=2.08mm~2.1mm

Hence, the minimum diameter of the eyepiece is 2.1 mm.

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Most popular questions from this chapter

Figure 34-30 shows four thin lenses, all of the same material, with sides that either are flat or have a radius of curvature of magnitude 10cm. Without written calculation, rank the lenses according to the magnitude of the focal length, greatest first.

A moth at about eye level is10鈥�cmin front of a plane mirror; a man is behind the moth,30鈥�cmfrom the mirror. What is the distance between man鈥檚 eyes and the apparent position of the moth鈥檚 image in the mirror?

In Fig. 34-26, stick figure O stands in front of a thin, symmetric lens that is mounted within the boxed region; the central axis through the lens is shown. The four stick figuresI1andI4suggest general locations and orientations for the images that might be produced by the lens. (The figures are only sketched in; neither their height nor their distance from the lens is drawn to scale.) (a) Which of the stick figures could not possibly represent images? Of the possible images, (b) which would be due to a converging lens, (c) which would be due to a diverging lens, (d) which would be virtual, and (e) which would involve negative magnification?

The formula 1p+1i=1f is called the Gaussian form of the thin-lens formula. Another form of this formula, the Newtonian form, is obtained by considering the distance xfrom the object to the first focal point and the distancex' from the second focal point to the image. Show thatxx'=f2 is the Newtonian form of the thin-lens formula

Figure 34-25 shows a fish and a fish stalker in water. (a) Does the stalker see the fish in the general region of point a or point b? (b) Does the fish see the (wild) eyes of the stalker in the general region of point c or point d?
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