Question

A travelling microscope is focussed on a mark on a piece of paper and the scale reading is A. A rectangular block of glass is placed on the paper and the microscope is raised and focussed the mark on the paper, then microscope reading is B. A layer of lycopodium powder is sprinkled on the block of glass, the reading now is C. The refractive index of the material of the block is:
A.)$\dfrac{{C - B}}{{C - A}}$
B.)$\dfrac{{C - A}}{{C - B}}$
C.)$\dfrac{{C - A}}{{B - A}}$
D.)$\dfrac{C}{{C - A}}$

Answer 1

Hint: lycopodium powder is added to the surface so that the top of the slab can be focused. Also, placing a glass slab raises the image slightly. Travelling microscope is used to measure the real and apparent depth of the spot.

Complete step-by-step answer:
This is a standard experiment used to find the refractive index of materials.
We know that when letters on a paper are viewed through a glass slab, they appear to be raised. The height to which an image rises depends on the refractive index of the slab, and is given by the relation:

$\mu = \dfrac{h}{{h'}}$

where $h$ is the actual depth of the letter and $h'$ is the apparent depth due to refraction.

In this experiment, the microscope first focuses on the ink spot without any glass slab. This gives the position of the actual ink spot.

Now, when the glass slab is placed, the image shifts upward and hence, the second reading gives the position of the apparent image.

Now to measure the real and apparent depths, we need to know the position of the top of the glass slab. But a microscope would not focus here since glass is transparent.
So lycopodium powder is added on the surface so that we have some reference to focus on.

Thus the last reading, taken after adding lycopodium on the surface, gives the position of the top surface of the slab.
Let's conclude the readings

A - position of the actual point
B - position of the apparent image
C - position of the top of the slab

Now it is clear from figure1 that the depth of real point would be
$h = A - C$
and that of apparent image would be
$h' = A - B$

Since $\mu = \dfrac{h}{{h'}}$ , we can substitute values from equations and to find the final answer.
$\mu = \dfrac{{A - C}}{{A - B}}$ Or equivalently $\dfrac{{C - A}}{{B - A}}$.

Note: The equation $\mu = \dfrac{h}{{h'}}$ is valid only for small angles of incidence, where the approximation\[\sin i \approx i \approx \tan i\] holds. So the microscope is placed on the top of the slab so that rays coming are not much deviated.