Light of certain wavelength in a vacuum has wavelength of 438 nm if it propagates in water and 390 nm if it propagates in benzene. Calculate the ratio of refractive index of water to the refractive index of benzene.
To calculate the ratio of refractive index between water and benzene, we need to use the formula:
n = c/v
Where:
- n is the refractive index
- c is the speed of light in vacuum (~ 299,792,458 m/s)
- v is the speed of light in a medium
First, we need to calculate the refractive index of water and benzene separately:
For water:
c = 299,792,458 m/s
v_water = c / lambda_water
where lambda_water = 438 nm = 438 x 10^-9 m
v_water = c / (438 x 10^-9 m)
For benzene:
c = 299,792,458 m/s
v_benzene = c / lambda_benzene
where lambda_benzene = 390 nm = 390 x 10^-9 m
v_benzene = c / (390 x 10^-9 m)
Now, we will calculate the ratio of refractive index:
n_water = c / v_water
n_benzene = c / v_benzene
Ratio = n_water / n_benzene
Let's substitute the values:
v_water = c / (438 x 10^-9 m)
v_benzene = c / (390 x 10^-9 m)
n_water = c / v_water
n_benzene = c / v_benzene
Ratio = n_water / n_benzene
Replace the values of v_water and v_benzene, and calculate the ratio of refractive index between water and benzene.