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.