Lens In Liquid

Description:

When lens is placed in air i.e. when lens is normally used. We have the following equation −

P_a = 1/f_a = (μ_g - μ_air/μ_air)(1/R₁ - 1/R₂) ...... (1)

Where,

P_a = Power of lens in air.

f_a = Focal length of lens in air.

μ_g = Refractive index of glass lens.

μ_air = Refractive index of air.

P_L = 1/f_L = (μ_g - μ_L/μ_L)(1/R₁ - 1/R₂) ...... (2)

Where,

P_L = Power of lens in liquid.

f_L = Focal length of lens in liquid.

μ_g = Refractive index of glass lens.

μ_L = Refractive index of liquid.

Dividing equation 2 by equation 1, we get −

P_L/P_a = f_a/f_L = (μ_g - μ_L/μ_L)(μ_air/μ_g - μ_air)

∴ f_L = f_aμ_L(μ_g - μ_air)/μ_air(μ_g - μ_L)

∴ f_L = μ_L(μ_g - 1)/(μ_g - μ_L)f_a

As μ_L is larger than 1, the denominator becomes smaller than the numerator i.e.

μ_L(μ_g - 1)/(μ_g - μ_L) > 1

Therefore,

f_L > f_a

As focal length of a lens in liquid is greater than the focal length in air i.e. power of lens in liquid is always smaller than the power of lens in air.

P_L > P_air

If the refractive index of liquid is equal to the refractive index of lens then the focal length of lens becomes infinity i.e. rays become parallel and power of lens is zero i.e. no refraction.

Note − If the refractive index of liquid is greater than the refractive index of lens then convex lens will become negative i.e. it will act as a concave lens.