Question

A plane glass is kept over a coloured word $\text{VIBGYOR}$, where the colour of letters are the same as the colours of components in white light. The letter which appears least raised is,

• A. $\text{R}$
• B. $\text{Y}$
• C. $\text{O}$
• D. $\text{V}$

Answer 1

The correct option is A $\text{R}$

We know that,
For air-glass medium, refractive index of glass,
$\mu =\frac{c}{v}=\frac{{\lambda }_o}{\lambda }$
So, $\mu \propto \frac{1}{\lambda }$ .............$\left(1\right)$
Also, $\text{apparent depth}=\frac{\text{real depth}}{\mu }$
So, $\text{apparent depth}\propto \frac{1}{\mu }$ .............$\left(2\right)$
From $\left(1\right)$ and $\left(2\right)$,
$\text{apparent depth}\propto \lambda$
Greater the value of wavelength, greater the apparent depth and least the object raised.
We know that the wavelength of red colour is greatest, thus, its apparent depth will be greatest, hence, the letter $\text{R}$ will appear least raised.

Why this question? The intent is to make you understand, '' the effect of wavelength of light on the refraction of light''. Tips: Same material will exhibit varying refractive index for different wavelengths.