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प्रश्न
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.
उत्तर
Magnifying power of simple microscope, when image is formed at DDV.
The magnifying power of simple microscope is defined as the ratio of the angle subtended at an eye by the image to the angle subtended at an unaided eye by the object kept at DDV.
`MP = beta/alpha = ("Angle subtended at an eye by the image" )/("Angle subtended at an unaided eye by the objectat DDV")`
`tan beta = (AB)/u = beta`
`tan alpha = (AB)/D = alpha`
`MP = (AB D)/(u AB) = D/u`
By lens formula `1/"v" - 1/u = 1/f`
But u and v are negative and f is positive , `1/u = 1/"v" + 1/f ⇒ D/u = D/"v" + D/f`
`MP = D/"v" + D/f`
At `"v" = DDV`
`MP = D/D + D/f`
`MP = 1 + D/f`
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संबंधित प्रश्न
Explain the basic differences between the construction and working of a telescope and a microscope
A compound microscope consists of an objective lens of focal length 2.0 cm and an eyepiece of focal length 6.25 cm separated by a distance of 15 cm. How far from the objective should an object be placed in order to obtain the final image at
- the least distance of distinct vision (25 cm), and
- infinity?
What is the magnifying power of the microscope in each case?
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(a) L < u
(b) L > u
(c) fo < L < 2fo
(d) L > 2fo
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Draw a ray diagram of compound microscope for the final image formed at least distance of distinct vision?
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. |
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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. |
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