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| | | ### Statement |
| | | |
| | − | $12.1.20.$ [Insert the problem statement] |
| | + | $12.1.20.$ |
| | | |
| | + | A layer of photoemulsion is applied on a mirror metal substrate. When light |
| | + | falls normally at a distance of 10−5mm from the metal surface, the emulsion |
| | + | becomes blackened. Explain this effect. Determine the wavelength of light |
| | + | incident on a metal surface. At what distance from the substrate surface will |
| | + | the second layer of blackened emulsion be located? |
| | + | |
| | | ### Solution |
| | | |
| | − | La luz que incide normalmente sobre el espejo metálico interfiere con la luz reflejada, generando una onda estacionaria. El campo eléctrico tiene un nodo en la superficie del metal ($E = 0$) y antinodos (máximos de intensidad) a distancias $\lambda/4, 3\lambda/4, 5\lambda/4, \dots$ de la superficie. La emulsión fotográfica se ennegrece en esos antinodos. |
| | | |
| | − | Longitud de onda |
| | + | Light incident normally on the metallic mirror interferes with the reflected light, generating a standing wave. The electric field has a node at the metal surface $(E = 0) $ and antinodes (intensity maxima) at distances $\lambda/4, 3\lambda/4, 5\lambda/4, \dots $from the surface. The photographic emulsion darkens at those antinodes. |
| | | |
| | − | El primer ennegrecimiento (primer antinodo) se produce a $d_1 = 10^{-5}\ \text{cm}$ . Como $ d_1 = \lambda/4 $: |
| | + | Wavelength |
| | | |
| | − | $\boxed{\lambda = 4 \times 10^{-5}\ \text{cm} = 400\ \text{nm}}$ |
| | + | The first darkening (first antinode) occurs at $d_1 = 10^{-5}\ \text{cm}$. Since $d_1 = \lambda/4$: |
| | | |
| | − | Distancia entre capas ennegrecidas |
| | + | $\boxed{\lambda = 4 \times 10^{-5}\ \text{cm} = 400\ \text{nm}}$. |
| | | |
| | − | Los antinodos consecutivos están separados media longitud de onda: |
| | + | Distance between darkened layers |
| | | |
| | − | $\boxed{x = \frac{\lambda}{2} = 2 \times 10^{-5}\ \text{cm}}$ |
| | + | Consecutive antinodes are separated by half a wavelength: |
| | | |
| | + | $\boxed{x = \frac{\lambda}{2} = 2 \times 10^{-5}\ \text{cm}}.$ |
| | + | |
| | | #### Answer |
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| | − | [Insert a concise answer or boxed result] |
| | + | |
| | + | $\boxed{\lambda = 4 \times 10^{-5}\ \text{cm} = 400\ \text{nm}}$. |
| | + | |
| | + | $\boxed{x = \frac{\lambda}{2} = 2 \times 10^{-5}\ \text{cm}}.$] |
