A convex lens of focal length 20 cm is made of glass of refractive index 1.5. When it is immersed in a liquid of refractive index 1.33, its focal len…

Lens maker's formula is $1/f = (\mu_{gl} - 1)(1/R_1 - 1/R_2)$. When immersed in liquid, $1/f_m = ((\mu_{gl}/\mu_m) - 1)(1/R_1 - 1/R_2)$. Taking the ratio: $f_m/f = (\mu_{gl} - 1) / ((\mu_{gl}/\mu_m) - 1) = (1.5 - 1) / ((1.5/1.33) - 1) \approx 0.5 / 0.128 \approx 3.9$. Thus $f_m \approx 3.9 \times 20 = 78\text{ cm}$.