Question

A spherical surface of radius 30 cm separates two transparent media A and B with refractive indices 1.33 and 1.48 respectively. The medium A is on the convex side of the surface. Where should a point object be placed in medium A so that the paraxial rays become parallel after refraction at the surface?

Answer 1

Given,
Spherical surface of radius (R) = 30 cm
Medium A has refractive index (μ₁) = 1.33
Medium B has refractive index (μ₂) = 1.48
Medium A is the convex side of surface.

Since,
We know that paraxial rays become parallel after refraction
i.e, the image of the point object will be formed at infinity.
Therefore v = ∞

Using the lens equation,
$$\begin{gathered} \frac{{\mathrm{\mu }}_2}{v}-\frac{{\mathrm{\mu }}_1}{u}=\frac{{\mathrm{\mu }}_2-{\mathrm{\mu }}_1}{\mathrm{R}} \\ \Rightarrow \frac{1.48}{\infty }-\frac{1.33}{u}=\frac{1.48-1.33}{30} \\ \Rightarrow -\frac{1.33}{u}-\frac{0.15}{30} \\ \therefore u=-266.0\mathrm{cm} \end{gathered}$$

Hence, the object is placed at a distance of 266.0 cm from the convex surface on side A.