Question

A plane glass slab is kept over various coloured letters, the letter which appears least raised is?

• A. Blue
• B. Green
• C. Red
• D. Violet

Answer 1

The correct option is C

Red

The explanation for the correct option.

1. The refractive index or index of refraction of a substance is a measure of the speed of light in that substance.
2. It is expressed as a ratio of the speed of light in a vacuum relative to that in the considered medium.
3. The wavelength and frequency of all colors are,

4. We can determine the required answer by using the relationship between wavelength and refractive index in relation to normal shift and the refractive index. The formula for refractive index is,

$\mathrm{\mu }=\frac{\mathrm{real}\mathrm{depth}}{\mathrm{apparent}\mathrm{depth}}$

5. According to Cauchy's formula, the refractive index depends on the wavelength of the light rays passing through it by the following relation.

$\mathrm{\mu }=\mathrm{A}+\frac{\mathrm{B}}{{\mathrm{\lambda }}^2}+\frac{\mathrm{C}}{{\mathrm{\lambda }}^4}$

Here, $\mathrm{\mu }$ is the refractive index, $\mathrm{\lambda }$ is the wavelength and $\mathrm{A},\mathrm{B}$ and $\mathrm{C}$ are constants.

6. The refractive index rises as the wavelength of light decreases and vice versa.

7. Inside a glass prism, the red colour would travel the first.

8. Since, out of the given colors in the options, red has the highest wavelength of all colors and hence will show minimal shift and red letters will appear to be raised least.

So,

${\mathrm{\lambda }}_{\mathrm{Violet}}<{\mathrm{\lambda }}_{\mathrm{Blue}}<{\mathrm{\lambda }}_{\mathrm{Green}}<{\mathrm{\lambda }}_{\mathrm{Red}}$,

${\mathrm{\mu }}_{\mathrm{Violet}}>{\mathrm{\mu }}_{\mathrm{Blue}}>{\mathrm{\mu }}_{\mathrm{Green}}>{\mathrm{\mu }}_{\mathrm{Red}}$

${\mathrm{A}}_{\mathrm{Red}}>{\mathrm{A}}_{\mathrm{Green}}>{\mathrm{A}}_{\mathrm{Blue}}>{\mathrm{A}}_{\mathrm{Violet}}$

Hence, option $\mathrm{C}$ is the correct answer.