Question

The velocity of light in air is 3 x ${10}^{8}m{s}^{-1}$ wavelenght of visible light is 400 nm to 800 nm(4000 $A^0$ to 8000 $A^0$). Its corresponding frequency is ___________$H_z$ to _______$H_z$

• A. 7.5 x ${10}^{14}$, 3.75 x ${10}^{14}$
• B. 6.3 x ${10}^{14}$, 2.3 x ${10}^{14}$
• C. 3 x ${10}^{14}$, 8 x ${10}^4$
• D. 0.4 x ${10}^{-8}$, 0.8 x ${10}^{-8}$

Answer 1

The correct option is A 7.5 x ${10}^{14}$, 3.75 x ${10}^{14}$

Velocity of wave is given as

$v=f\lambda$

where $f=$ frequency

and $\lambda =$ wavelength

Case $\left(1\right)$

$v=3\times {10}^{8}m{s}^{-1}$

$\lambda =4000\mathring{A}=400\times {10}^{-9}m$

As we know, $f\lambda =v$

$\therefore f=\frac{v}{\lambda }$

$=\frac{3\times {10}^8}{400\times {10}^{-9}}$

$=.75\times {10}^{13}{H}_z$

$f=7.5\times {10}^{14}{H}_z$

Case $2$

$v=3\times {10}^{8}m{s}^{-1}$

$\lambda =8000\mathring{A}=800\times {10}^{-9}m$

$f=\frac{v}{\lambda }$

$=\frac{3\times {10}^8}{800\times {10}^{-9}}$

$\cong 0.38\times {10}^{-13}{H}_z$

$\cong 3.8\times {10}^{14}{H}_z$

$\therefore$ Option (A) is the correct answer.