Question

A hollow double concave lens is made of very thin transparent material. It can be filled with air or either of the two liquids ${{L}_{1}}$ or ${{L}_{2}}$ having refractive indices ${{n}_{1}}$ and ${{n}_{2}}$, respectively (${{n}_{2}}>{{n}_{1}}>1$). The lens will diverge parallel beams of light if it is filled with.
1. Air and placed in air
2. Air and immersed in ${{L}_{1}}$
3. ${{L}_{1}}$ and immersed in ${{L}_{2}}$
4. ${{L}_{2}}$ and immersed in ${{L}_{1}}$

Answer 1

Hint: Study the type and working of a concave lens. Try to understand how light passes through this type of lens and how the path of light depends on the refractive index of the lens and the medium where the lens is placed.

Complete step-by-step answer:
A concave lens is a lens with two concave surfaces on each side of the lens. It is also called a diverging lens because it diverges the incoming parallel light rays on the condition that the refractive index of the medium on which the lens is placed should be lower than the refractive index of the material of the lens.
Now, considering the first option, the lens is filled with air and the medium at which lens is placed is also air. So, the refractive index of both the lens and the medium is the same. So, we will not get any diverging beam from this condition. The beams will remain parallel.
In the second option, lens is filled with air and the lens is placed in the medium of liquid ${{L}_{1}}$ with refractive index ${{n}_{1}}$ which is greater than the refractive index of air. So, in this case also we won’t get any diverging beams.
Considering the third option, the lens is filled with liquid ${{L}_{1}}$ with refractive index ${{n}_{1}}$ and is placed in a medium filled with liquid ${{L}_{2}}$ with refractive index ${{n}_{2}}$ . according to the question the refractive index of the medium is greater than the refractive index of the material of the lens. so, it can’t fulfil the requirement.
Considering the fourth option, the lens is filled with liquid ${{L}_{2}}$ with refractive index ${{n}_{2}}$ and is placed in a medium filled with liquid ${{L}_{1}}$ with refractive index ${{n}_{1}}$ here the refractive index of the medium is less than the refractive index of the lens. . So, it fulfils the condition for divergence of light beams in a concave lens.
The correct option is (D).

Note: Depending on the refractive index of the lens and the medium where it is placed the properties of the lens can change from converging to diverging. In the above question when we are considering option two and three, the refractive index of the medium is less than the refractive index of the lens. So, here we will obtain that for this two condition the lens will converge the light beam