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Question
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.
Solution
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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