To determine how many times longer the wavelength of red light is compared to the wavelength of violet light, we need to calculate the ratio of the two wavelengths.
1. Let’s denote the wavelength of red light as [tex]\( \lambda_{red} \)[/tex].
[tex]\[
\lambda_{red} = 8 \times 10^{-7} \text{ meters}
\][/tex]
2. Let’s denote the wavelength of violet light as [tex]\( \lambda_{violet} \)[/tex].
[tex]\[
\lambda_{violet} = 4 \times 10^{-7} \text{ meters}
\][/tex]
3. To find out how many times longer the wavelength of red light is compared to violet light, we divide the wavelength of red light by the wavelength of violet light.
[tex]\[
\text{Ratio} = \frac{\lambda_{red}}{\lambda_{violet}} = \frac{8 \times 10^{-7}}{4 \times 10^{-7}}
\][/tex]
4. Simplifying this ratio:
[tex]\[
\frac{8 \times 10^{-7}}{4 \times 10^{-7}} = \frac{8}{4} \times \frac{10^{-7}}{10^{-7}} = 2 \times 1 = 2
\][/tex]
So, the wavelength of red light is 2 times as long as the wavelength of violet light.
Therefore, the correct answer is:
- 2 times as long
