A lens of refractive index ' ' has focal length ' f '. When the lens is immersed in a liquid of refractive index ' ₀ ', its focal length becomes ' f₀ '. Then ' f₀ ' is given by

Step-by-step solution

Using the lens maker's formula for the lens in air: 1 f = ( - 1) ( 1 R₁ - 1 R₂ ) When the lens is immersed in a liquid of refractive index ₀ , the relative refractive index of the lens becomes ₀ . The focal length f₀ in the liquid is given by: 1 f₀ = ( ₀ - 1 ) ( 1 R₁ - 1 R₂ ) 1 f₀ = ( - ₀ ₀ ) ( 1 R₁ - 1 R₂ ) Dividing the first equation by the second equation: f₀ f = - 1 - ₀ ₀ f₀ f = ₀( - 1) - ₀ f₀ = ₀( - 1)f - ₀ Answer: ₀( -1)f ( - ₀)