Question

In one experiment, 6000 photons are detected in a O.10-mm- wide strip where the amplitude of the electromagnetic wave is 200 V/m. What is the wave amplitude at a nearby 0.20-mm-wide strip where 3000 photons are detected?

Short answer

Hence, the wave amplitude at 0.20mm wide strip is$100V/m$

Step-by-step solution

Given information

In one experiment, 6000 photons are detected in a O.10-mm- wide strip where the amplitude of the electromagnetic wave is 200 V/m.

Explanation

The first strip's photon count is given by

$N_1=\frac{H{I}_1\delta x_1}{hf}\left(1\right)\hspace{0.17em}$

Count for second strip is:

role="math" localid="1648587585729" $N_2=\frac{H{I}_2\delta x_2}{hf}\left(2\right)$

Dividing (1) by (2):

$\frac{N_1}{N_2}=\frac{H{I}_1\delta x_1}{H{I}_2\delta x_2}=\frac{I_1\delta x_1}{I_2\delta x_2}$

Calculations 

We have the values as:

$N_1=6000,n_2=3000,I_1={200}^2,I_2=?,\delta x_1=0.1\mathrm{mm}\text{and}\delta x_2=0.2\mathrm{mm}$

Substituting the values,

$$\begin{gathered} \frac{6000}{3000}=\frac{{200}^2\times 0.1}{I_2\times 0.2} \\ {I}_2=100V/m \end{gathered}$$