In Young's double slit experiment, green light `(lambda=5461Å)` is used and 60 fringes were seen in the field view. Now sodium light is used `(lambda=5890Å)` , then number of fringes observed are

Options

A. 40
B. 60
C. 50
D. 55

Explanation

To solve the problem, we will use the relationship between the number of fringes observed in Young's double slit experiment and the wavelength of light used. The number of fringes \( n \) is inversely proportional to the wavelength \( \lambda \).

### Step 1: Understand the relationship between the number of fringes and wavelength
The relationship can be expressed as:
\[ \frac{n_1}{n_2} = \frac{\lambda_2}{\lambda_1} \]
where:
- \( n_1 \) is the number of fringes observed with wavelength \( \lambda_1 \)
- \( n_2 \) is the number of fringes observed with wavelength \( \lambda_2 \)

### Step 2: Identify the given values
From the problem:
- \( n_1 = 60 \) (number of fringes with green light)
- \( \lambda_1 = 5461 \, \text{Å} \) (wavelength of green light)
- \( \lambda_2 = 5890 \, \text{Å} \) (wavelength of sodium light)

### Step 3: Rearrange the formula to find \( n_2 \)
We can rearrange the formula to solve for \( n_2 \):
\[ n_2 = n_1 \cdot \frac{\lambda_1}{\lambda_2} \]

### Step 4: Substitute the values into the equation
Now, substitute the known values into the equation:
\[ n_2 = 60 \cdot \frac{5461}{5890} \]

### Step 5: Calculate \( n_2 \)
Now, we perform the calculation:
1. Calculate the fraction:
\[ \frac{5461}{5890} \approx 0.928 \]
2. Multiply by \( n_1 \):
\[ n_2 \approx 60 \cdot 0.928 \approx 55.68 \]

Since the number of fringes must be a whole number, we round this to:
\[ n_2 \approx 55 \]

### Final Answer
The number of fringes observed with sodium light is approximately **55**.

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