A monochromatic ray of light passes from air to glass. The wavelength of light in air is `lamda`, the speed of light in air is c and in glass is V. if the refractive index of glass is `1*5`, write down (a) the relationship between c and V, (b) the wavelength of light in glass.

Answer

To solve the problem step by step, we will use the concepts of refractive index and the relationship between the speed of light and wavelength in different media.

### Step 1: Understanding Refractive Index
The refractive index (n) of a medium is defined as the ratio of the speed of light in a vacuum (or air) to the speed of light in that medium. Mathematically, it can be expressed as:
\[ n = \frac{c}{V} \]
where:
- \( n \) is the refractive index of the medium (in this case, glass),
- \( c \) is the speed of light in air,
- \( V \) is the speed of light in glass.

### Step 2: Relationship Between c and V
Given that the refractive index of glass is 1.5, we can write:
\[ 1.5 = \frac{c}{V} \]

To express the relationship between \( c \) and \( V \), we can rearrange this equation:
\[ V = \frac{c}{1.5} \]

### Step 3: Wavelength of Light in Different Media
The wavelength of light in a medium is related to its speed and frequency. The relationship can be expressed as:
\[ \lambda = \frac{V}{f} \]
where:
- \( \lambda \) is the wavelength,
- \( V \) is the speed of light in the medium,
- \( f \) is the frequency of the light.

Since the frequency of light remains constant when it passes from one medium to another, we can denote the wavelength in air as \( \lambda \) and the wavelength in glass as \( \lambda_g \).

### Step 4: Wavelength in Glass
Using the relationship of wavelength and speed, we can express the wavelength in glass as:
\[ \lambda_g = \frac{V}{f} \]

Since we know that \( V = \frac{c}{1.5} \), we can substitute this into the equation for \( \lambda_g \):
\[ \lambda_g = \frac{\frac{c}{1.5}}{f} \]

Now, we also know that:
\[ \lambda = \frac{c}{f} \]

Thus, we can express \( \lambda_g \) in terms of \( \lambda \):
\[ \lambda_g = \frac{\lambda}{1.5} \]

### Final Answers:
(a) The relationship between \( c \) and \( V \) is:
\[ V = \frac{c}{1.5} \]

(b) The wavelength of light in glass is:
\[ \lambda_g = \frac{\lambda}{1.5} \]