An equi-convex lens (of refractive index 1.50) is placed in contact with a liquid layer on top of a plane mirror as shown. A small needle with its tip on the principal axis is moved along the axis until its inverted image is found at the position of the needle. The distance of the needle from the lens is measured to be 45.0 cm. The liquid is removed and the experiment is repeated. The new distance is measured to be 30.0 cm. What is the refractive index of the liquid?

Question

Philoid · Accepted Answer

The focal length of lens of glass is 30 cm.

And that of liquid lens is f(say).

Now by the equation,

Or,

so, f = - 90 cm.

Now, using lens maker’s formula,

Putting, μ=1.5, R₁=-R₂=R, we get, R=30 cm.

For, liquid lens, R₁=-30 cm and R₂. Applying again is Lens maker’s we get,

μ = 4/3.