Question

A glass concave lens is placed in a liquid in which it behaves like a converging lens. If the refractive index of glass and water wrt air

Answer 1

A glass concave lens is placed in a liquid in which it behaves like a converging lens. If the refractive index of glass is less than that of liquid.

explanation : we know, concave lens spreads out light rays that have been refracted through it. so, a concave lens is diverging lens. hence, focal length of concave lens, f < 0

it behaves like a converging lens only when focal length of it will be positive.

using formula,

1/f = (μ2/μ1 - 1)[1/R1 - 1/R2]

in air, it behaves like a diverging lens.

so, 1/f = (μ2/1 - 1) [1/R1 - 1/R2] < 0

as we know, (μ2 - 1) > 0 [ generally, refractive index is greater than 1 ]

so, [1/R1 - 1/R2] < 0 .......(1)

in liquid it behaves like a converging lens.

so, 1/f = (μ2/μ1 - 1)[1/R1 - 1/R2] > 0

from equation (1),

[1/R1 - 1/R2] < 0

so, (μ2/μ1 - 1) < 0

⇒μ2/μ1 < 1

⇒μ2 < μ1

hence, refractive index of liquid should be greater than refractive index of glass.

also read : Refractive index of convex lens material is 1.46.the refractive index of Benzene and water are 1.5 and 1.0 respectively...

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A double concave lens with refractive index (n)=1.5 is kept in the air. It's two spherical surfaces have radii R1 =20cm ...

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Answer 2

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it behaves like a converging lens only when focal length of it will be positive. in air, it behaves like a diverging lens. in liquid it behaves like a converging lens. hence, refractive index of liquid should be greater than refractive index of glass