Question

A printed page is kept pressed by a glass cube (\[\mu = 1.5\]) of edge 6 cm. By what amount will the printed letters appear to be shifted when viewed from the top?
A. 1.5 cm
B. 3 cm
C. 6 cm
D. 2 cm

Answer 1

Hint: Due to refraction of light from rare medium to denser medium, the depth of the glass cube is different from the real depth. The refractive index is the ratio of real depth to apparent depth.

Formula used:
\[\mu = \dfrac{{{\text{Real depth}}}}{{{\text{Apparent depth}}}}\]
Here, \[\mu \] is the refractive index.

Complete step by step answer:
We know that, when a light ray travels from rarer medium to denser medium, it bends towards the normal. Therefore, as we see from the top of the glass cube (denser medium), the depth of the letters will be less than the original depth of the letters.

We have, the refractive index of the glass is,
\[\mu = \dfrac{{{\text{Real depth}}}}{{{\text{Apparent depth}}}}\]
\[{\text{Apparent depth}} = \dfrac{{{\text{Real depth}}}}{\mu }\]

We have given, the edge of the cube is 6 cm that is real depth. Therefore, the apparent depth will be,
 \[{\text{Apparent depth}} = \dfrac{{{\text{6}}\,{\text{cm}}}}{{1.5}}\]
\[ \Rightarrow {\text{Apparent depth}} = 4\,cm\]

Therefore, the shift in the position of the letters is, \[6\,cm - 4\,cm = 2\,cm\].

So, the correct answer is “Option D”.

Additional Information:
The real-life example of this case is the apparent depth of the swimming pool. Water has a greater refractive index than the air, therefore, the depth of the swimming pool we see is less than the real depth. So, you must be extra careful in the swimming pool if you don’t know how to swim.

Note:
Other method to solve this question is to use the formula for the shift in the thickness,\[\Delta t = \left( {1 - \dfrac{1}{\mu }} \right)t\], where, t is the original thickness and \[\mu \] is the refractive index of the material.