Light is incident on a glass plate of refractive index 3.0 such that angle of refraction is 60° .Dark band is observed corresponding to the wavelength of 12000 A .If the thickness of glass plate is `1.2`x`10^(-3)` mm. Calculate the order of the interference band for reflected system.

Answer

To solve the problem step by step, we will follow the provided information and apply the relevant formula for interference in reflected light.

### Step 1: Write down the given data
- Refractive index (μ) = 3.0
- Angle of refraction (r) = 60°
- Wavelength (λ) = 12000 Å (angstrom)
- Thickness of the glass plate (t) = 1.2 x 10^(-3) mm

### Step 2: Convert the units to SI
- Convert thickness from mm to meters:
\[ t = 1.2 \times 10^{-3} \text{ mm} = 1.2 \times 10^{-3} \times 10^{-3} \text{ m} = 1.2 \times 10^{-6} \text{ m} \]

- Convert wavelength from angstroms to meters:
\[ \lambda = 12000 \text{ Å} = 12000 \times 10^{-10} \text{ m} = 12 \times 10^{-7} \text{ m} \]

### Step 3: Use the formula for dark bands in reflected light
The condition for dark bands in reflected light is given by:
\[ 2 \mu t \cos r = n \lambda \]
Where:
- n = order of interference band

### Step 4: Rearranging the formula to find n
From the equation, we can express n as:
\[ n = \frac{2 \mu t \cos r}{\lambda} \]

### Step 5: Calculate cos(r)
For r = 60°:
\[ \cos(60°) = \frac{1}{2} \]

### Step 6: Substitute the values into the equation
Now substituting the values into the equation for n:
\[ n = \frac{2 \times 3.0 \times 1.2 \times 10^{-6} \times \frac{1}{2}}{12 \times 10^{-7}} \]

### Step 7: Simplify the expression
Calculating the numerator:
\[ 2 \times 3.0 \times 1.2 \times 10^{-6} \times \frac{1}{2} = 3.0 \times 1.2 \times 10^{-6} = 3.6 \times 10^{-6} \]

Now, substituting into the equation for n:
\[ n = \frac{3.6 \times 10^{-6}}{12 \times 10^{-7}} = \frac{3.6}{12} \times 10^{1} = 0.3 \times 10^{1} = 3 \]

### Step 8: Conclusion
The order of the interference band (n) for the reflected system is:
\[ \boxed{3} \]