# A symmetric bicon

Given

Focal length of convex lens f1 = y

Refractive index of lens μ1 = 1.5

Let focal length of liquid be f2

And refractive index of liquid be μ2.

Let the focal length of system (lens + liquid) be f = x(given)

Now equivalent focal length is given as

Let radius of curvature of lens be R.

Then for a convex lens R1 = R and R2 = -R

From lens maker formula

Substituting the value of f1 and μ1, to find R

Since liquid acts as a plane mirror, therefore, R1 = R = ycm and R2 = ∞.

Applying lens maker formula for liquid, we get

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