A light wave has a frequency of $4 \times 10^{14} Hz$. Find the difference in its wavelengths in alcohol of refractive index 1.35 and glass of refractive index 1.5:

556 Å

The correct answer is Option (4) → 556 Å

The relation between the wavelength, (v) frequency and (n) refractive index -

$λ=\frac{c}{nθ}$

where,

$c=3×10^8m/s$ (Speed of light)

$v=4×10^{14}Hz$

for alcohol,

$λ_{alcohol}=\frac{c}{n_{alcohol}×v}=\frac{3×10^8}{1.55×4×10^{14}}$

$=556nm$

for glass,

$λ_{glass}=\frac{c}{n_{glass}×v}=\frac{3×10^8}{1.5×4×10^{14}}$

$=500nm$

$∴λ_{alcohol}-λ_{glass}=556-500$

$=56nm$