Question

A thin convex lens of focal length $f$ made of crown glass is immersed in a liquid of refractive index ${\mu }_r.({\mu }_l>{\mu }_c)$ where ${\mu }_c$ is the refractive index of the crown glass.
The convex lens now is

• A. A convex lens of longer focal length
• B. A convex lens of shorter focal length
• C. A divergent lens
• D. A convex lens of focal length $({\mu }_c-{\mu }_l)f$

Answer 1

The correct option is C A divergent lens

Using len's maker formula :
Focal length of lens in liquid $\frac{1}{F}=(\frac{{\mu }_c}{{\mu }_l}-1)(\frac{2}{R})$
$\therefore$ $\frac{1}{F}=\left(\frac{{\mu }_c-{\mu }_l}{{\mu }_l}\right)(\frac{2}{R})$
Since ${\mu }_c<{\mu }_l$
$⟹F<0$
Thus the given convex lens becomes divergent lens in the liquid.