Advertisements
Advertisements
Question
A small telescope has an objective lens of focal length 150 cm and an eye piece of focal length 5 cm. If this telescope is used to view a 100 m high tower 3 km away, find the height of the final image when it is formed 25 cm away from the eye piece.
Advertisements
Solution
The formula for magnifying power is,
Magnifying power, `M = -f_0/f_e (1+f_e/D)`
where, f0 = Focal length of the objective = 150 cm
fe = Focal length of the eye-piece = 5cm
D = Least distance of distinct vision = 25 cm
`M = -150/5 xx (1+5/25) =-36`
`M =beta/alpha`
`M = tan beta/tan alpha`(As angles α and β are small)
`tan alpha =( \text{Height of object})/(\text { Distance of object from objective}) = H/u = 100/3000 = 1/30`
`M =tan beta/((1/30))`
`tan beta = (-36)/30`
`tan beta = (\text{Height of image})/(\text { Distance of image formation}) = (H')/D`
Thus,
`H' = (-36 xx 25)/30 = -30 cm`
Negative sign indicates that we get an inverted image.
APPEARS IN
RELATED QUESTIONS
Why should the objective of a telescope have large focal length and large aperture? Justify your answer.
You are given the following three lenses. Which two lenses will you use as an eyepiece and as an objective to construct an astronomical telescope ? Give reason
| Lenses | Power (D) | Aperture (cm) |
| L1 | 3 | 8 |
| L2 | 6 | 1 |
| L3 | 10 | 1 |
You are given three lenses of power 0.5 D, 4 D, and 10 D to design a telescope.
1) Which lenses should be used as objective and eyepiece? Justify your answer.
2) Why is the aperture of the objective preferred to be large?
With regard to an astronomical telescope of refracting type~ state how you will increase its:
1) magnifying power
2) resolving power
Write the two important factors considered to increase the magnifying power?
"A telescope resolves whereas a microscope magnifies." Justify this statement ?
Draw a labelled ray diagram of an astronomical telescope to show the image formation of a distant object. Write the main considerations required in selecting the objective and eyepiece lenses in order to have large magnifying power and high resolution of the telescope.
Read the following paragraph and answer the questions.
| A number of optical devices and instruments have been designed and developed such as periscope, binoculars, microscopes and telescopes utilising the reflecting and refracting properties of mirrors, lenses and prisms. Most of them are in common use. Our knowledge about the formation of images by the mirrors and lenses is the basic requirement for understanding the working of these devices. |
- Why the image formed at infinity is often considered most suitable for viewing. Explain
- In modern microscopes, multicomponent lenses are used for both the objective and the eyepiece. Why?
- Write two points of difference between a compound microscope and an astronomical telescope
OR
Write two distinct advantages of a reflecting type telescope over a refracting type telescope.
An optical instrument that uses objective and eyepiece lenses to magnify distant terrestrial or celestial objects is called a:
In the working idea of a telescope's magnifying power, the beam of incident rays is inclined at an angle \[\alpha\] with the principal axis, while the emergent beam is inclined at a greater angle \[\beta\]. This produces:
