Question

For diamond, if critical angle is ${30}^{\circ }$ (outside medium is air with $\mu =1$), then speed of light in diamond and wavelength of yellow colour in diamond (${\lambda }_{yellowinair}=600nm$) are respectively

• A. $1.5\times {10}^{8}m/s,300nm$
• B. $1.5\times {10}^{8}m/s,600nm$
• C. $6\times {10}^{8}m/s,300nm$
• D. $1.5\times {10}^{8}m/s,1200nm$

Answer 1

The correct option is A $1.5\times {10}^{8}m/s,300nm$

${\theta }_c={30}^{\circ }$
$\sin {\theta }_c=\frac{{\mu }_{rarer}}{{\mu }_{denser}}=\frac{1}{2}$
$\Rightarrow {\mu }_{diamond}=2$
We know,
$\mu =\frac{c}{v}$

$v=\frac{c}{\mu }=\frac{3\times {10}^8}{2}=1.5\times {10}^{8}m/s$

${\lambda }^{\prime }=\lambda /\mu =600/2=300nm$