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Question
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.
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Solution
A compound microscope consists of two convex lenses co-axially separated by some distance. The lens nearer to the object is called the objective. The lens through which the final image is viewed is called the eyepiece.
Magnifying power, when final image is at infinity:
The magnification produced by the compound microscope is the product of the magnifications produced by the eyepiece and objective.
`∴M = M_e xx M_0 ...... (1)`
Where, Me and M0 are the magnifying powers of the eyepiece and objective respectively.
If u0 is the distance of the object from the objective and v0 is the distance of the image from the objective, then the magnifying power of the
objective is `M_0 = (h')/h =L/f_0 ( using tanβ = (h/f_0) = =(h/L))`
Where, h, h' are object and image heights respectively and f0 is the focal length of the objective.
L is the tube length i.e. the distance between the second focal point of the objective and the first focal point of the eyepiece.
When the final image is at infinity, `M_e = D/f_e`
Magnifying power of compound microscope,`M = M_0 xx M_e = L/f_0 xx D/f_e`
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| 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. |
A compound microscope consists of an objective of 10X and an eye-piece of 20X. The magnification due to the microscope would be:
| 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:
