Question

The focal length of a convex lens dipped in a liquid of same refractive index as that of the lens, will:

• A. Become zero
• B. Become infinite
• C. Become small, but non-zero
• D. Remain unchanged

Answer 1

Answer: (B)

Lens maker's formula is given by,
$\frac{1}{f}=({\left(\mu \right)}_2-{\left(\mu \right)}_1)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)$ , where ${\mu }_2$ is the refractive index of the material of lens and ${\mu }_1$ is the refractive index of the medium in which lens is being kept.
If ${\mu }_1={\mu }_2$ . Then,
$\frac{1}{f}=({\left(\mu \right)}_2-{\left(\mu \right)}_2)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)\Rightarrow \frac{1}{f}=0\Rightarrow f=\infty$
Then lens behaves like a plane surface with focal length infinity.