According to the lens maker's formula, the focal length of a lens placed in a medium of refractive index $n_1$ is given by $$\frac{1}{f}=\left(\frac{n_2}{n_1}-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right).$$ If $n_2=n_1$, what follows?
AThe lens becomes a perfect reflector
BThe focal length becomes infinite, so the lens behaves like a plane glass sheet
CThe focal length becomes zero, so all rays meet at the optical centre
DThe power doubles because both media are identical
Answer & Solution
Correct answer: B. The focal length becomes infinite, so the lens behaves like a plane glass sheet
If $n_2=n_1$, then $\left(\frac{n_2}{n_1}-1\right)=0$, so $\frac{1}{f}=0$. Hence $f\to\infty$ and the power $P=1/f$ becomes zero. The lens then produces no net convergence or divergence and behaves like a plane transparent sheet.
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