Question

It is found that all electro-magnetic signals sent from A towards B reach point C inside the glass sphere, as shown in fig. The speed of electromagnetic signals in glass cannot be

• A. $1.0\times {10}^{8}m{s}^{-1}$
• B. $2.4\times {10}^{8}m{s}^{-1}$
• C. $2\times {10}^{7}m{s}^{-1}$
• D. $4\times {10}^{7}m{s}^{-1}$

Answer 1

Answer: (B)

$2.4\times {10}^{8}m{s}^{-1}$

For the electromagnetic signals to not refract outside the sphere, refractive index must be greater than critical refractive index for total internal reflection, i.e., $\mu >{\mu }_{cr}=\frac{1}{\sin i}$

Here $i={45}^{\circ }$

This gives $\mu >\sqrt{2}$

Hence the speed of signals $<\frac{c}{\mu }=2.1213\times {10}^{8}m{s}^{-1}$