Calculating Light Intensity Transmission

The problem asks for the final intensity of light after passing through three identical sheets, each absorbing 20% of the light that hits it.

Understanding Light Absorption and Transmission

• Each sheet absorbs 20% of incident light. This means 20% of the light energy is lost or converted.
• The percentage of light transmitted by a single sheet is the remaining portion: 100% - 20% = 80%.
• In decimal form, the transmission factor for one sheet is $1 - 0.20 = 0.80$.

Step-by-Step Calculation

1. Transmission through the first sheet: The intensity is multiplied by the transmission factor. Intensity after 1st sheet = Initial Intensity $\times 0.80$
2. Transmission through the second sheet: The light transmitted by the first sheet becomes the incident light for the second sheet. Intensity after 2nd sheet = (Intensity after 1st sheet) $\times 0.80$ Intensity after 2nd sheet = (Initial Intensity $\times 0.80$) $\times 0.80$ = Initial Intensity $\times (0.80)^2$
3. Transmission through the third sheet: Similarly, the light transmitted by the second sheet is incident on the third. Intensity after 3rd sheet = (Intensity after 2nd sheet) $\times 0.80$ Intensity after 3rd sheet = (Initial Intensity $\times (0.80)^2$) $\times 0.80$ = Initial Intensity $\times (0.80)^3$
4. Final Calculation: Calculate the value of $(0.80)^3$. $(0.80)^3 = 0.80 \times 0.80 \times 0.80 = 0.64 \times 0.80 = 0.512$
5. Convert to Percentage: To express the final transmitted intensity as a percentage of the initial intensity, multiply by 100. Final Transmission Percentage = $0.512 \times 100\% = 51.2\%$

Conclusion

After passing through three sheets, each absorbing 20% of the light, the transmitted light intensity is 51.2% of the original intensity.