Thin Lenses — Question 4

Question 4

A surrounding liquid can weaken or reverse a glass lens

A thin lens of glass index ng=1.50 has focal length 20 cm in air. In a uniform surrounding medium of index nm, use $1/f=(n_g/n_m-1)G$, where $G=1/R_1-1/R_2$ is fixed by its shape.

1. Find G and the focal length in index nm=1.25.

2. Find the focal length in index nm=1.60 and classify the lens behavior.

Question 4 - Solution

A surrounding liquid can weaken or reverse a glass lens

(a) Method and calculation

$$1/(20\,\mathrm{cm})=(1.50-1)G\Rightarrow\boxed{G=0.10\,\mathrm{cm^{-1}}}.$$$$1/f=(1.50/1.25-1)(0.10)=0.020\Rightarrow\boxed{f=50\,\mathrm{cm}}.$$

(b) Interpretation and further calculation

$$1/f=(1.50/1.60-1)(0.10)=-0.00625\,\mathrm{cm^{-1}}.$$$$\boxed{f=-160\,\mathrm{cm}}\quad\text{diverging in the higher-index surrounding medium}.$$

Physical check

Lens shape alone does not determine convergence; the refractive-index contrast controls the sign of the power.