Question

What will be the effect on focal length and nature of convex lens of refractive index \( n = \frac{3}{2} \) dipped in a liquid of refractive index \( n = \frac{3}{2} \)?

Hint:

When the refractive indices of the lens and the surrounding medium are equal, the lens loses its ability to focus light, and its focal length becomes infinite.

Answer 1

When a convex lens with a refractive index \( n_1 = \frac{3}{2} \) is immersed in a liquid with a refractive index \( n_2 = \frac{3}{2} \), the refractive index difference between the lens and the surrounding medium becomes zero. The focal length \( f \) of a lens is given by the formula: \[ \frac{1}{f} = (n_1 - n_2) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \] where \( n_1 \) is the refractive index of the lens and \( n_2 \) is the refractive index of the surrounding medium. Since \( n_1 = n_2 \), the refractive index difference \( (n_1 - n_2) \) becomes zero. This implies that the lens loses its focusing power, and the focal length becomes infinite. The lens effectively behaves as if it is not present in the system, and no image will be formed. Therefore, the nature of the lens becomes neutral, and it no longer functions as a converging lens.