An equiconvex lens of refractive index μ 2 is used between two mediums of different refractive index μ 1 and μ 3 as shown. The system acts as a diverging lens if (considering paraxial rays)

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An equiconvex lens of refractive index μ 2 ​ is used between two mediums of different refractive index μ 1 ​ and μ 3 ​ as shown. The system acts as a diverging lens if (considering paraxial rays)

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For a lens between two media, add the powers of the two refracting surfaces: $P = \frac{μ _{2} - μ _{1}}{R _{1}} + \frac{μ _{3} - μ _{2}}{R _{2}}$ . Equiconvex lens: $R_{1} = + R, R_{2} = - R$ , so $P = \frac{2 μ _{2} - μ _{1} - μ _{3}}{R}$ . Diverging needs $P < 0$ , i.e. $2 μ_{2} < μ_{1} + μ_{3}$ . (A) $2 (2.4) = 4.8 < 1.2 + 3.8 = 5.0$ diverging. (B) $2 \times \frac{5}{3} = \frac{10}{3} < 3 + 2 = 5$ diverging. (C) $2 \times \frac{7}{2} = 7 > \frac{3}{2} + \frac{5}{2} = 4$ converging. (D) $2 \times \frac{10}{3} = \frac{20}{3} > \frac{5}{3} + \frac{4}{3} = 3$ converging.

Hence (A) and (B).

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