Advertisements
Advertisements
Question
A compound microscope consists of an objective of focal length 1 cm and an eyepiece of focal length 5 cm. An object is placed at a distance of 0.5 cm from the objective. What should be the separation between the lenses so that the microscope projects an inverted real image of the object on a screen 30 cm behind the eyepiece?
Advertisements
Solution
For the compound microscope, we have:
Focal length of the objective, f0 =1.0 cm Focal length of the eyepiece, fe = 5 cm Distance of the object from the objective, u0 =0.5 cm
Distance of the image from the eyepiece, ve =30 cm
The lens formula for the objective lens is given by
`1/v_0 -1/u_0 = 1/f_0`
`=> 1/v_0 +1/0.5 =1/1`
`=>1/v_0 =1 -10/5 =-1`
⇒ v0= -1 cm
The objective will form a virtual image at the side same as that of the object at a distance of 1 cm from the objective lens. The image formed by the objective will act as a virtual object for the eyepiece.
The lens formula for the eyepiece is given by
`1/v_e -1/u_e =1/f_e`
`=> 1/30 -1/u_e =1/5`
`=> -1/u_e =1/5 -1/30 =(6-1)/30 =1/6`
⇒ ue = -6 cm
∴ Separation between the objective and the eyepiece = 6 − 1 = 5 cm
APPEARS IN
RELATED QUESTIONS
Draw a labelled ray diagram showing the formation of a final image by a compound microscope at least distance of distinct vision
An angular magnification (magnifying power) of 30X is desired using an objective of focal length 1.25 cm and an eyepiece of focal length 5 cm. How will you set up the compound microscope?
You are given the following three lenses. Which two lenses will you use as an eyepiece and as an objective to construct a compound microscope?
| Lenses | Power (D) | Aperture (cm) |
| L1 | 3 | 8 |
| L2 | 6 | 1 |
| L3 | 10 | 1 |
How can the resolving power of a compound microscope be increased? Use relevant formula to support your answer.
Draw a ray diagram showing the image formation by a compound microscope. Hence obtained expression for total magnification when the image is formed at infinity.
Distinguish between myopia and hypermetropia. Show diagrammatically how these defects can be corrected.
The focal length of the objective of a compound microscope if fo and its distance from the eyepiece is L. The object is placed at a distance u from the objective. For proper working of the instrument,
(a) L < u
(b) L > u
(c) fo < L < 2fo
(d) L > 2fo
A simple microscope is rated 5 X for a normal relaxed eye. What will be its magnifying power for a relaxed farsighted eye whose near point is 40 cm?
A simple microscope using a single lens often shows coloured image of a white source. Why?
A lady uses + 1.5 D glasses to have normal vision from 25 cm onwards. She uses a 20 D lens as a simple microscope to see an object. Find the maximum magnifying power if she uses the microscope (a) together with her glass (b) without the glass. Do the answers suggest that an object can be more clearly seen through a microscope without using the correcting glasses?
Draw a neat labelled ray diagram showing the formation of an image at the least distance of distinct vision D by a simple microscope. When the final image is at D, derive an expression for its magnifying power at D.
A convex lens of a focal length 5 cm is used as a simple microscope. Where should an object be placed so that the image formed by it lies at the least distance of distinct vision (D = 25 cm)?
How does the resolving power of a microscope change when
(i) the diameter of the objective lens is decreased?
(ii) the wavelength of the incident light is increased ?
Justify your answer in each case.
In the case of a regular prism, in minimum deviation position, the angle made by the refracted ray (inside the prism) with the normal drawn to the refracting surface is ______.
With the help of a ray diagram, show how a compound microscope forms a magnified image of a tiny object, at least distance of distinct vision. Hence derive an expression for the magnification produced by it.
| A compound microscope consists of two converging lenses. One of them, of smaller aperture and smaller focal length, is called objective and the other of slightly larger aperture and slightly larger focal length is called eye-piece. Both lenses are fitted in a tube with an arrangement to vary the distance between them. A tiny object is placed in front of the objective at a distance slightly greater than its focal length. The objective produces the image of the object which acts as an object for the eye-piece. The eye-piece, in turn, produces the final magnified image. |
In a compound microscope, the images formed by the objective and the eye-piece are respectively.
| A compound microscope consists of two converging lenses. One of them, of smaller aperture and smaller focal length, is called objective and the other of slightly larger aperture and slightly larger focal length is called eye-piece. Both lenses are fitted in a tube with an arrangement to vary the distance between them. A tiny object is placed in front of the objective at a distance slightly greater than its focal length. The objective produces the image of the object which acts as an object for the eye-piece. The eye-piece, in turn, produces the final magnified image. |
The focal lengths of the objective and eye-piece of a compound microscope are 1.2 cm and 3.0 cm respectively. The object is placed at a distance of 1.25 cm from the objective. If the final image is formed at infinity, the magnifying power of the microscope would be:
