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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 34-37 gives the lateral magnification mof an object versus the object distanc pfrom a spherical mirror as the object is moved along the mirror鈥檚 central axis through a range of values p. The horizontal scale is set by Ps=10.0mm. What is the magnification of the object when the object is 21cm from the mirror?

An object is 30.0cmfrom a spherical mirror, along the mirror鈥檚 central axis. The mirror produces an inverted image with a lateral magnification of absolute value 0.500. What is the focal length of the mirror?

A narrow beam of parallel light rays is incident on a glass sphere from the left, directed toward the center of the sphere. (The sphere is a lens but certainly not a thin lens.) Approximate the angle of incidence of the rays as 0掳, and assume that the index of refraction of the glass is n<2.0(a) In terms of n and the sphere radius r, what is the distance between the image produced by the sphere and the right side of the sphere? (b) Is the image to the left or right of that side? (Hint: Apply Eq. 34-8 to locate the image that is produced by refraction at the left side of the sphere; then use that image as the object for refraction at the right side of the sphere to locate the final image. In the second refraction, is the object distance positive or negative?)

An object is 10.0 mm from the objective of a certain compound microscope. The lenses are 300 mm apart, and the intermediate image is 50.0 mm from the eyepiece. What overall magnification is produced by the instrument?

32 through 38 37, 38 33, 35 Spherical refracting surfaces. An object Ostands on the central axis of a spherical refracting surface. For this situation, each problem in Table 34-5 refers to the index of refraction n1where the object is located, (a) the index of refraction n2on the other side of the refracting surface, (b) the object distance p, (c) the radius of curvature rof the surface, and (d) the image distance i. (All distances are in centimeters.) Fill in the missing information, including whether the image is (e) real (R)or virtual (V)and (f) on the same side of the surface as the object Oor on the opposite side.
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