A ray of light of frequency is 5.09 x 10^14 Hz is traveling from water to medium X. The angle of incidence in water is 45 degrees and the angle of refraction in Medium X is 29 degrees. The index of refraction of Medium X is 1.94. Calculate the wavelength for each medium. What material is medium X?
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To calculate the wavelength in each medium, we can use the formula:
wavelength = speed of light / frequency
1. Calculate the wavelength in water:
The speed of light in vacuum is approximately 3.00 x 10^8 meters per second (m/s). However, since light is traveling in water, which has a refractive index, we need to modify the formula as follows:
wavelength in water = speed of light in vacuum / (refractive index of water * frequency)
The refractive index of water is approximately 1.33.
wavelength in water = (3.00 x 10^8 m/s) / (1.33 * 5.09 x 10^14 Hz)
2. Calculate the wavelength in Medium X:
The refractive index of Medium X is given as 1.94.
wavelength in Medium X = (3.00 x 10^8 m/s) / (1.94 * 5.09 x 10^14 Hz)
Now, let's perform the calculations:
1. wavelength in water = (3.00 x 10^8) / (1.33 * 5.09 x 10^14) = approximately 3.72 x 10^-7 meters or 372 nm
2. wavelength in Medium X = (3.00 x 10^8) / (1.94 * 5.09 x 10^14) = approximately 3.29 x 10^-7 meters or 329 nm
Based on the calculated values, the wavelength in water is approximately 372 nm, and the wavelength in Medium X is approximately 329 nm.
To identify the material of Medium X, we need to compare its refractive index with known values for different materials. Unfortunately, the information provided is insufficient to determine the specific material.