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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