A printed page is kept pressed by a glass cube (µ = 1.5) of edge 6.0 cm. By what amount will the printed letters appears to be shifted when viewed from top ?

Question

Accepted Answer

To determine the apparent shift in the position of the printed letters when viewed through a glass cube, we need to consider the concept of refraction. The apparent shift can be calculated using the formula for lateral shift in a medium:

$$ \text{Shift} = t \left(1 - \frac{1}{\mu}\right) $$

where:
- $ t $ is the thickness of the medium (in this case, the edge of the cube, which is 6.0 cm),
- $ \mu $ is the refractive index of the medium (given as 1.5 for the glass cube).

Substituting the given values into the formula:

$$ \text{Shift} = 6.0 \, \text{cm} \left(1 - \frac{1}{1.5}\right) $$

$$ \text{Shift} = 6.0 \, \text{cm} \left(1 - \frac{2}{3}\right) $$

$$ \text{Shift} = 6.0 \, \text{cm} \left(\frac{1}{3}\right) $$

$$ \text{Shift} = 2.0 \, \text{cm} $$

Thus, the printed letters appear to be shifted by 2.0 cm when viewed from the top through the glass cube. This calculation confirms that Option 2 is indeed the correct answer.

Now, let's explain why the other options are incorrect:

1. **Option 1 (1.0 cm):** This option is incorrect because the calculation using the formula for lateral shift clearly shows that the shift is 2.0 cm, not 1.0 cm. The refractive index and the thickness of the cube do not support a shift of only 1.0 cm.

2. **Option 3 (3.0 cm):** This option is incorrect because the calculated shift of 2.0 cm is less than 3.0 cm. The formula and the given values do not result in a shift as large as 3.0 cm.

3. **Option 4 (6.0 cm):** This option is incorrect because a shift of 6.0 cm would imply that the letters appear to be at the same level as the top surface of the cube, which is not possible given the refractive index of the glass. The shift is only a fraction of the cube's thickness, as calculated.

In conclusion, the correct answer is Option 2, with a shift of 2.0 cm, as supported by the calculation using the principles of refraction.