the no of wave in 6cm of vacum
is same as that of no of wave in xcm of medium refractive index of given medium is 3/2 find the value of x
To determine the value of x, we need to use the formula for the number of waves in a given distance.
The formula to calculate the number of waves is:
Number of waves = Distance / Wavelength
In this case, we know that the distance is 6 cm for the vacuum and we need to find the value of x for the medium with a refractive index of 3/2.
Since the refractive index affects the wavelength, we need to consider the relationship between the refractive index (n), wavelength (λ), and the speed of light (c):
n = c / v
where c is the speed of light in vacuum, and v is the speed of light in the medium.
As the refractive index for the given medium is 3/2, we can rewrite the equation as:
3/2 = c / v
Next, we need to determine how the wavelength changes in the given medium. The refractive index directly affects the wavelength:
n = λ0 / λ
where λ0 is the wavelength in vacuum, and λ is the wavelength in the medium.
Substituting the given values:
3/2 = λ0 / λ
To solve for λ, we can rearrange the equation:
λ = λ0 * (2/3)
Now we have the relationship between the wavelengths in vacuum and the medium.
Substituting this value of wavelength into the formula for the number of waves, we have:
Number of waves in vacuum (6 cm) = Number of waves in medium (x cm)
Distance / Wavelength_in_vacuum = Distance / Wavelength_in_medium
6 cm / λ0 = x cm / λ
Substituting the value of λ = λ0 * (2/3), we get:
6 cm / λ0 = x cm / (λ0 * (2/3))
Now, we can simplify the equation:
6 cm * (2/3) = x cm
4 cm = x
Therefore, the value of x is 4 cm.