Question

The ratio of amplitude of electric field to the amplitude of the magnetic field associated with an electromagnetic wave propagating in glass \((n=1.5)\) is :

• A. \(3\times10^{8}\,\text{ms}^{-1}\)
• B. \(2\times10^{8}\,\text{ms}^{-1}\)
• C. \(3.3\times10^{-9}\,\text{ms}^{-1}\)
• D. \(5\times10^{-9}\,\text{ms}^{-1}\)

Hint:

Always remember: \[ \frac{E_0}{B_0}=c \] in vacuum and \[ \frac{E_0}{B_0}=v=\frac{c}{n} \] inside a medium of refractive index \(n\).

Answer 1

The Correct Option is B

Concept: An electromagnetic wave consists of mutually perpendicular electric and magnetic fields. For an electromagnetic wave propagating in a medium, the ratio of the electric field amplitude to the magnetic field amplitude is equal to the speed of the wave in that medium. Thus, \[ \frac{E_0}{B_0}=v. \] The speed of light in a medium of refractive index \(n\) is \[ v=\frac{c}{n}, \] where \[ c=3\times10^8\,\text{ms}^{-1} \] is the speed of light in vacuum.

Step 1: Write the relation between refractive index and speed. The refractive index is given by \[ n=\frac{c}{v}. \] Rearranging, \[ v=\frac{c}{n}. \]

Step 2: Substitute the given values. Given, \[ n=1.5 \] and \[ c=3\times10^8\,\text{ms}^{-1}. \] Therefore, \[ v=\frac{3\times10^8}{1.5}. \]

Step 3: Perform the calculation. \[ v=2\times10^8\,\text{ms}^{-1}. \] Thus, \[ \frac{E_0}{B_0} = 2\times10^8\,\text{ms}^{-1}. \]

Step 4: Identify the correct option. Hence, \[ \boxed{\frac{E_0}{B_0}=2\times10^8\,\text{ms}^{-1}} \] and therefore \[ \boxed{\text{(B)}} \] is the correct answer.