Final answer:
The ratio of the two wavelengths in Young's double-slit experiment where the fourth maximum for one wavelength coincides with the fifth maximum for the other is 5:4. This is derived using the formula for double-slit interference maxima positions.
Step-by-step explanation:
The student's question relates to Young's double-slit experiment, which is used to calculate the ratio of two wavelengths based on the position of their respective interference maxima. According to the rules of double-slit interference, the position of the bright fringes on the screen is given by d sin(θ) = mλ, where d is the slit separation, θ is the angle, m is the order of the maximum, and λ is the wavelength.
In the scenario where the fourth maximum of one wavelength coincides with the fifth maximum of another, we have d sin(θ) = 4λ1 = 5λ2. Hence, the ratio of the two wavelengths λ1 to λ2 is 5:4. This ratio indicates that the first wavelength is slightly longer than the second one.
This concept is critical for understanding wave optics and the interference of light, and helps in determining the characteristics of light based on the interference patterns observed in Young's experiment.