Question

A thin convex lens made from crown glass $(\mu =\frac{3}{2})$ has focal length f. When it is measured in two different liquids having refractive indices $\frac{4}{3}$ and $\frac{5}{3}$, it has the focal lengths $f_1$ and $f_2$ respectively. The correct relation between the focal lengths is:

• A. $f_2>f$ and $f_1$ becomes negative
• B. $f_1$ and $f_2$ both become negative
• C. $f_1=f_2<f$
• D. $f_1>f$ and $f_2$ becomes negative

Answer 1

Answer: (D)

$f_1>f$ and $f_2$ becomes negative

Using lens makers formula and taking ratios,$\frac{f_m}{f}=\frac{(\mu -1)}{(\frac{\mu }{{\mu }_m}-1)}$

$\Rightarrow \frac{(\frac{3}{2}-1)}{(\frac{3/2}{4/3}-1)}=4$

$\Rightarrow f_1=4f$

$\frac{f_2}{f}=\frac{(\frac{3}{2}-1)}{(\frac{3/2}{5/3}-1)}=-5$

$\Rightarrow f_2<0$