Experiment: To set up an astronomical telescope and find its magnifying power.
Astronomical telescope consists of two converging lenses. One is the objective lens O of a long focal length fo. The other is the eye lens E of short focal length fe. A distant object is seen through it by keeping the objective lens towards that object. For simplicity, assume that the axis of the telescope EO points towards the base A of the distant object AB situated far beyond the figure. The objective lens makes a real, inverted and diminished image A’B’ of that object.
As the rays enter the eye lens, A’B’ functioning as the new object, its virtual magnified image A’B’ is formed. Thus, you observe fine details in A’B’ by the eye lens. The image A’B’ is at the focus of lens O and also is approximately at the focus of lens E. Therefore, separation between the lenses is
OE = fo = fe
Magnifying power of the telescope is angle subtended by the image A"B" at E divided by the angle subtended by the object AB at O.
m = fo/fe
In order to observe the image of distant object through the telescope, your eye should not be too close to the eye lens E. This lens makes a real image of lens O at I. It is just beyond the outer focal point Fe of the lens E.
All light rays entering through O and passing through lens E, also pass through this image. This is called the exit pupil of the telescope. Pupil of your eye must coincide with this image in order to receive all the light coming through objective and the eye lens. This enables you to see all the objects that the telescope is capable of seeing at one time.
An optical bench with three lens - uprights, objective lens (f = 50 cm to 80 cm, diameter - 50 mm), eye lens (f = 5 cm to 10 cm diameter = 20 mm to 50 mm), circular cardboard diaphram (O.D. - 50 mm, central hole diameter - 15 mm), a scale with bold marks, metre scale
(A) Setting up the Telescope
1. Find the focal length of the objective Lens fo, by focussing the image of a distant bright object on a screen, or on a wall of your laboratory and measuring its distance from the lens. Similarly, find the focal length of eye lens fe. These are only approximate values.
2. Calculate approximate distance between the two lenses, f0 + fe, for telescope making.
3. Fix the eye lens in one upright and keep it at the 10 cm mark on the optical bench.
4. Mark a small cross (×) in the centre of the objective lens. Fix it on another upright. Adjust the height of its centre above optical bench equal to that of the eye lens. Then keep it on the optical bench at a distance f0 + fe from the eye lens.
5. Fix the diaphram D in the third upright. Adjust the height of its centre above optical bench equal to that of the eye lens. Then keep it on the optical bench at a distance slightly more than fe from the eye lens on the side opposite to the objective lens. You should now see the image of cross mark on objective lens made by eye piece at the centre of the diaphram.
Make fine adjustments in the position of diaphram vertically, horizontally and along length of the optical bench. Thus you locate the exit pupil of the telescope.
6. Now point this telescope to any distant object. Keep your eye at the hole in diaphram D and look at inverted image of the object. You will have to move the diaphram a little forward. You may also have to adjust the position of lenses O and E a little in order to focus a sharp image of the object.
(B) Finding the Magnifying Power
7. Keep the scale with bold marks vertical in front of the telescope at a distance of at least 10 m. If your laboratory is not long enough, do this part of experiment in the corridor.
8. Adjust the position of eye lens so that the final virtual image of the scale is roughly at the same distance as the scale seen directly, For this adjustment you may look by one eye (say the right eye) into the telescope and by the other eye look directly at the scale. When proper adjustment is done, you see the scale and its magnified image together, as if stuck to each other.
9. Your scale with bold marks is such that it can be seen clearly by your left eye at a distance of upto 20 m. Observe on it the size of the enlarged image of one smallest division seen through the telescope by the right eye. Ratio of the size of this enlarged image to size of the division gives the magnifying power of the telescope.
10. Repeat the observation of step (9) for two divisions of the scale, three divisions of the scale, and so on. Thus obtain a few more measured values of magnifying power. Find the mean of all these values.
1. fo and fe have been measured only approximately.
2. Expression m = f0/fe is valid only for the case when object-and its final virtual image are both at infinity. But it is not so in the experiment.
3. Lenses used in the experiment are not achromatic. Thus image seen in the telescope made in the experiment is not quite sharp as it would be in a standard telescope using achromatic lenses, Thus magnifying power cannot be found quite accurately.