Question

A plane glass plate is placed over various coloured letters (violet, green, yellow, red). The letter which appears to be raised more
A. Red
B. Yellow
C. Green
D. Violet

Answer 1

Hint: We need to know how the normal shift of light ray is related to the wavelength of the light passing through a medium. By using the relation between refractive index and wavelength in the relation between normal shift and the refractive index, we can find the required answer.

Complete answer:
We are given four colours, out of which violet has the minimum wavelength while red has the maximum wavelength.
In order to answer this question, we know information about the following relations:
The normal shift taking place in the light rays passing through a glass plate having a thickness t is given as
$d = t\left( {1 - \dfrac{1}{\mu }} \right)$
Here $\mu $ signifies the refractive index of the glass and with increase in the value of the refractive index the value of normal shift also increases and vice-versa. The refractive index depends on the wavelength of the light rays passing through it by the following relation.
$\mu = A + \dfrac{B}{{{\lambda ^2}}}$
Here A and B are constant while $\lambda $ is the wavelength of the light. With decrease in the wavelength of light, the value of the refractive index increases and vice-versa.
Now out of the given colours, violet has the smallest wavelength of all colours and hence will show maximum shift and violet letters will appear to be raised more.

Hence, the correct answer is option D.

Note:
It should be noted that on comparing the two relations that we have used above, we can say that the normal shift is inversely related to the wavelength of the light passing through the medium. Due to which the colour having largest wavelength will have the smallest shift while the colour having shortest wavelength will have the largest shift.