Question

It is found that electromagnetic signals sent inside glass sphere from A towards B reach diametrically opposite point C. The speed of electromagnetic signals in glass cannot be:

• A. $1.0\times {10}^8\text{m/s}$
• B. $2.4\times {10}^8\text{m/s}$
• C. $2\times {10}^7\text{m/s}$
• D. $4\times {10}^7\text{m/s}$

Answer 1

The correct option is B $2.4\times {10}^8\text{m/s}$


For the electro-magnetic signals to not refract outside the sphere, refractive index must be greater than critical refractive index for total internal reflection. i.e.,
$\mu >{\mu }_{cr}$
${\mu }_{cr}=\frac{1}{\text{sin i}}=\frac{1}{\text{sin}{45}^{\circ }}$
${\mu }_{cr}=\sqrt{2}$
This gives
$\mu >\sqrt{2}$
Hence the speed of signals
$v<\frac{C}{\mu }$
$v<\frac{3\times {10}^8}{\sqrt{2}}\text{m/s}$
$v<2.12\times {10}^8\text{m/s}$
Hence, value in option (B) can not be the speed of signals