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 ______.

पर्याय

• 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:

`1/"f" = (("H"_"lens")/"M"_"liquid" - 1)2/"R"`

`1/"f" = ((3//2)/1 - 1)2/"R"`

`1/"f" = ((3//2)/1 - 1)2/"R"`     ...(i)

`1/"f"_1 = ((3//2)/(4//3) - 1) 2/"R"`   ...(ii)

From (i) and (ii)

`"f"_1/"f" = 4 => "f"_1 = 4"f"`