Q133 / 160 · TS EAMCET 2015 · Physics

A convex lens of glass $\left(\mu_g=1.45\right)$ has a focal length $f_a$ in air. The lens is immersed in a liquid of refractive index $\left(\mu_l\right) 1.3$. The ratio of the $f_1 / f_a$ is

  • Correct answer
    A
    3.9
  • B
    0.23
  • C
    0.43
  • D
    0.39

Solution

Focal length of lens when placed in air $$ F_{\text {air }}=\left(\mu_{\text {lens }}-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right) $$ Focal length of lens when placed in water $$ F_{\text {air }}=\left(\frac{\mu_{\text {lens }}}{\mu_{\text {liq }}}-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right) $$ Dividing Eq. (i) by Eq. (ii) $$ \frac{F_{\text {liq }}}{F_{\text {air }}}=\frac{(1.45-1)}{\left(\frac{1.45}{1.3}-1\right)}=\frac{0.45}{0.15} \times 1.3=3.9 $$

Hence, the correct answer is option: 'A'.

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