Q13 of 51 Page 345

A small telescope has an objective lens of focal length 144cm and an eyepiece of focal length 6.0cm. What is the magnifying power of the telescope? What is the separation between the objective and the eyepiece?

Given:


Focal length of the objective lens, fo = 144 cm
Focal length of the eyepiece, fe = 6.0 cm



The magnifying power of the telescope is given as,


…(1)


Where,


f0 = focal length of objective lens


fe = focal length of eyepiece


By putting the values in equation (1) we get,


⇒ m = 144/6


⇒ m = 24


The separation between the objective lens and the eyepiece is calculated as:


d = fo + fe


⇒ d = 144 + 6


⇒ d = 150cm


Hence 24 is the magnifying power of the telescope and the separation between the objective lens and the eyepiece is 150cm.


NOTE: Separation of lenses or length of telescope in case of refractive telescopes is always equal to the sum of focal lengths of the two lenses because one lens converges the rays from infinity at its focus and the eyepiece magnifies the image formed( virtual object) at its focus.


More from this chapter

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11

A compound microscope consists of an objective lens of focal length 2.0cm and an eyepiece of focal length 6.25cm separated by a distance of 15cm. How far from the objective should an object be placed in order to obtain the final image at (a) the least distance of distinct vision (25cm), and (b) at infinity? What is the magnifying power of the microscope in each case?

 12

A person with a normal near point (25cm) using a compound microscope with objective of focal length 8.0 mm and an eyepiece of focal length 2.5cm can bring an object placed at 9.0mm from the objective in sharp focus. What is the separation between the two lenses? Calculate the magnifying power of the microscope.

 14

(a) A giant refracting telescope at an observatory has an objective lens of focal length 15m. If an eyepiece of focal length 1.0cm is used, what is the angular magnification of the telescope?

(b) If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens? The diameter of the moon is 3.48 × 106m, and the radius of lunar orbit is 3.8 × 108m.

 15

Use the mirror equation to deduce that:

(a) an object placed between f and 2f of a concave mirror produces a real image beyond 2f.


(b) a convex mirror always produces a virtual image independent of the location of the object.


(c) the virtual image produced by a convex mirror is always diminished in size and is located between the focus and the pole.


(d) an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image.


[Note: This exercise helps you deduce algebraically properties of images that one obtains from explicit ray diagrams.]