1.

Draw a labelled diagram showing image formation by a simple microscope when the image is being formed at least distance of its distinct vision. Find an expression for its angular magnification (or the magnifying power.

Answer»

Solution :A simple microscope is a convex lens of small focal length f. The lens is HELD near the object AB at a small distance w(zz The ANGULAR magnification is defined as the ratio of the ANGLE subtended by the image (`beta`) to the angle subtended by the object, if placed at distance D for comfortable viewing (`ALPHA`) (or when seen directly).

`therefore` Angular magnification `m=beta/alpha =(ANGLEA.CB.)/(angleA_(0)CB.) = (angleACB)/(angleA_(0)CB.)`
As values of angles `alpha` and `beta` are extremely small, hence `alpha = tan alpha` and `beta= tan beta`.
`therefore m=beta/alpha =(tan beta)/(tan alpha) = (tan angleACB)/(tan angleA_(0)CB) =(AB//BC)/(AB//B.C) =(B.C)/(BC) =D/u` [since `A_(0)B. = AB`]
From lens formula, we have :
`1/(-D) -1/(-u) =1/f`
`rArr 1/u =1/f + 1/D = (D+f)/(Df)`
`therefore m=Du =D[(D+f)/(Df)] =(D+f)/f=1+D/f`
Thus, magnifying power of microscope will be more if focal length of microscope lens is less,


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