Question

You have three slabs of the same dimensions-the first one is hollow and completely filled with water, the second one is made up of crown glass and the third flint glass. If each of them has a colored mark at the bottom, in which case it will appear to have risen the most? Given its ${n_{{\text{flint}}}} > {n_{{\text{crown}}}} > {n_{{\text{water}}}}$.

Answer 1

Use the formula for the refractive index of the medium in terms of real depth and apparent depth. Hence, determine the relation between the refractive index and apparent depth. Also use the relation between the apparent depth and the shift. Hence, we will get the relation between the refractive index and shit which will give the information that the maximum shift is related to which slab.

Formula used:
The refractive index of the medium is given by
$n = \dfrac{{{\text{Real depth}}}}{{{\text{Apparent depth}}}}$

Complete answer:
We have given that there are three slabs having the same dimensions.The first slab is hollow and completely filled with water, the second slab is made up of crown glass and the third slab is made up of the flint glass.There is a colored mark at the bottom of all three slabs. We have asked to determine for which of the three slabs, the colored mark will appear to shift the most.We have given that the refractive index of the slab made up of flint glass is the most, the refractive index of water is the least and the refractive indices related to three slabs are related as:
${n_{{\text{flint}}}} > {n_{{\text{crown}}}} > {n_{{\text{water}}}}$

From equation (1), we can conclude that the refractive index of the medium is inversely proportional to the apparent depth and we know that the apparent depth is inversely proportional to the shift of the colored mark as the shift of the mark is upwards.Thus, we can say that the shift of the colored mark is directly proportional to refractive index of the medium.Since the refractive index of the flint glass is maximum amongst all three slabs, the colored mark will rise the most in the slab made up of flint glass.

Hence, the shift will be maximum for the slab of flint glass.

Note: The students should be careful while solving the question. The students may think that the apparent depth is inversely proportional to the refractive index. Hence, the maximum shift will be in the slab containing water. But we have asked to determine which slab shows the maximum shift in the position of colored mark and not the apparent depth of the mark. Hence, one should not forget to derive the relation between the refractive index and shift.