Two monochromatic beams $A$ and $B$ of equal intensity $I$, hit a screen. The number of photons hitting the screen by beam $A $ is twice that by beam $ B$. Then what inference can you make about their frequencies ?
Two monochromatic beams $A$ and $B$ of equal intensity $I$, hit a screen. The number of photons hitting the screen by beam $A $ is twice that by beam $ B$. Then what inference can you make about their frequencies ?
Intensity of light is given by,
$\mathrm{I}=\frac{\mathrm{E}_{n}}{\mathrm{~A} t}=\frac{n h f}{\mathrm{~A} t}$
(Where $A=$ area of given screen)
$\therefore \mathrm{I}=n^{\prime} hf$
where $n^{\prime}=\frac{n}{\mathrm{~A} t}=$ no. of photons incident on unit area of screen per unit time
$\therefore n^{\prime} f=\frac{\mathrm{I}}{h}=$ constant $(\because$ Here $\mathrm{I}$ is constant $)$
$\therefore n_{\mathrm{A}}^{\prime} f_{\mathrm{A}}=n_{\mathrm{B}}^{\prime} f_{\mathrm{B}}$
$\therefore\left(2 n_{\mathrm{B}}^{\prime}\right) f_{\mathrm{A}}=n_{\mathrm{B}}^{\prime} f_{\mathrm{B}} \quad$ (As per the statement)
$\therefore f_{\mathrm{A}}=\frac{f_{\mathrm{B}}}{2}$
$\Rightarrow$ Frequency of beam $A$ would be half of frequency of beam $B$.
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