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Asked in GSEB Board August 2020 · Lens maker's formula and power
Given: a glass lens of refractive index 1.47, to be made invisible in a liquid.
Idea: a clear object is seen only because light bends where it enters and leaves. Stop the bending and there is nothing to see.
In a liquid, 1/f = ((nₗₑₙₛ)/(n_liquid)-1)(1/(R₁)-1/(R₂)).
The radii are fixed, so the power is zero only when n_liquid = nₗₑₙₛ = 1.47.
Then light crosses both surfaces without deviating, no boundary can be seen, and the lens vanishes -- glycerine over ordinary crown glass is the classroom version of the trick.
So the liquid has refractive index 1.47.
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