Question

A convex lens with radii of curvature R₁ = R₂ is immersed in water. Assuming that the refractive indices of glass and water are 3/2 and 4/3 respectively, its focal length f₁ in comparison to that in air, f, is ______.

विकल्प

• f₁ = 4f

• f₁ = 2f

• f₁ = f/4

• f₁ = f

Answer 1

A convex lens with radii of curvature R₁ = R₂ is immersed in water. Assuming that the refractive indices of glass and water are 3/2 and 4/3 respectively, its focal length f₁ in comparison to that in air, f, is f₁ = 4f.

Explanation:

${\displaystyle \frac{1}{\text{f}}=(\frac{{\text{H}}_{\text{lens}}}{{\text{M}}_{\text{liquid}}}-1)\frac{2}{\text{R}}}$

${\displaystyle \frac{1}{\text{f}}=(\frac{3/2}{1}-1)\frac{2}{\text{R}}}$

${\displaystyle \frac{1}{\text{f}}=(\frac{3/2}{1}-1)\frac{2}{\text{R}}}$     ...(i)

${\displaystyle \frac{1}{{\text{f}}_1}=(\frac{3/2}{4/3}-1)\frac{2}{\text{R}}}$   ...(ii)

From (i) and (ii)

${\displaystyle \frac{{\text{f}}_1}{\text{f}}=4\Rightarrow {\text{f}}_1=4\text{f}}$