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Asked in GSEB Board July 2017 · Lens formula and magnification
Given: a thin convex lens whose image is half the height of the object, so |m|=1/2.
Idea: a convex lens makes a diminished image only when it is real and inverted, so m=v/u=-1/2. Writing the object distance as u=-d gives v=+d/2.
Put these into the lens formula 1/v-1/u=1/f:
2/d+1/d=1/f, that is 3/d=1/f.
So the object distance is d=3f.
That is sensible: 3f lies beyond 2f, which is exactly the region where a convex lens forms a real, inverted, diminished image.
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