Question

The left end of a long glass rod 5.82 cm in diameter has a convex hemispherical surface 2.91 cm in radius.The refractive index of the glass is 1.60. The rod is immersed in a liquid. An object 88.8 cm from the vertex of the left end of the rod and on its axis is imaged at a point 1.64 m inside the rod.

What is the refractive index of the liquid?

Answer 1

The problem can be depicted as shown above, where the given parameters can be stated interms of the above give n notation as shown: (note the sign convention is already included in the formula so we are stating the absolute values of the parameters only):

µ₁ = 1.60 (given refractive index of glass)

µ₂ = ? ( To be found out)

u = distance of object from the vertex = 88.8 cm

v = distance of image from vertex = 1.64 m = 164 cm

R = 2.91 cm

Using snell's law and approximating the angles we get the following formula:

On substituting we get

µ₂ = 1.58