Question

A lens behaves as a converging lens in air and diverging lens in water. The refractive index of the material of the lens is:
(A) 1
(B) Between 1 and 1.33
(C) 1.33
(D) Greater than 1.33

Answer 1

Hint: In order to answer this question, first we will write the refractive index when a lens behaves as a converging lens in air on the basis of the refractive index of air, similarly we will write the refractive index when a lens behaves as a diverging lens in air.


Complete step by step solution:
A lens behaves as a converging lens in air, so its refractive index is greater than 1:
$\mu > 1$ , because the refractive index of air is equal to 1.
A converging lens directs light to a spot near the lens' optical centre or axis. A lens that provides a true image by converting parallel light beams to convergent light rays. The image is actual and inverted as long as the object is outside of the focal point. The image becomes virtual and upright when the object is inside the focal point.
And the lens is also behaves as a diverging lens in water, so its refractive index is less than 1.33:
$\mu < 1.33$ , because the refractive index of water is equal to 1.33.
A diverging lens diverts light away from the lens's optical centre or axis. The negative lens is also known as a diverging lens. Diverging lenses come in a variety of designs, but they all have a negative sign that indicates that the image is virtual. A lens is a refractory transmissive optical device that alters the focus of a light beam.
Therefore, the refractive index of the material of the lens is between 1 and 1.33.
Hence, the correct option is (B) Between 1 and 1.33.

Note:
 The slower the speed of light is, the more optically dense the substance is. The refractive index is one such measure of a medium's optical density. The refractive index has no dimensions. It's a number that indicates how much slower a light wave would travel through a substance than it would in a vacuum.