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Asked in GSEB Board March 2022 · Lens maker's formula and power
Idea: a lens is seen only because light is refracted and partly reflected where its refractive index differs from that of the surroundings.
In a medium the lens maker's formula carries the factor ((nₗₑₙₛ)/(n_medium)-1).
That factor is zero when n_medium=nₗₑₙₛ; then 1/f=0 and the lens has infinite focal length.
The glass has n=1.5, so the liquid must also have n=1.5.
Light then passes straight through the trough and the lens cannot be seen, although it is still there.
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