Which of the statements are true, If a convex lens is placed in water:
a. Its focal length increases.
b. Its focal length decreases.
c. Rays bend less when they move through lens.
d. There is no change in radius of curvature.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → a, c, d
The lens maker’s formula in a medium is \( \displaystyle\frac{1}{f} = \left(\frac{\mu_g}{\mu_m}-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right) \). Water has a larger refractive index than air, so the ratio \( \mu_g/\mu_m \) is smaller in water than in air.
(a) Its focal length increases — True. The factor \( \left(\frac{\mu_g}{\mu_m}-1\right) \) becomes smaller, so \( 1/f \) falls and \( f \) increases (for glass of index 1.5 in water of index 4/3 it becomes four times as large).
(b) Its focal length decreases — False. It is the opposite of (a).
(c) Rays bend less when they move through lens — True. The bending at each surface depends on the relative refractive index, which is smaller between glass and water than between glass and air; the lens is weaker.
(d) There is no change in radius of curvature — True. The radii depend only on the shape of the lens surfaces, not on the surrounding medium.