In Young's double-slit experiment, the slit separation is 0.5 mm and the screen is 0.5 m away from the slit. For a monochromatic light of wavelength 500 nm, the distance of 3rd maxima from the 2nd minima on the other side of central maxima is

Options

A. 2.75 mm
B. 2.5 mm
C. 22.5 mm
D. 2.25 mm

Explanation

To solve the problem step by step, we will follow the principles of Young's double-slit experiment and the concepts of fringe width, maxima, and minima.

### Step 1: Identify the given values
- Slit separation (d) = 0.5 mm = \(0.5 \times 10^{-3}\) m
- Distance from the slits to the screen (D) = 0.5 m
- Wavelength of light (λ) = 500 nm = \(500 \times 10^{-9}\) m

### Step 2: Calculate the fringe width (β)
The formula for fringe width (β) in Young's double-slit experiment is given by:
\[ \beta = \frac{\lambda D}{d} \]
Substituting the values:
\[ \beta = \frac{(500 \times 10^{-9} \text{ m})(0.5 \text{ m})}{0.5 \times 10^{-3} \text{ m}} \]
Calculating this gives:
\[ \beta = \frac{(500 \times 10^{-9} \times 0.5)}{0.5 \times 10^{-3}} = 500 \times 10^{-6} \text{ m} = 0.5 \text{ mm} \]

### Step 3: Determine the positions of the maxima and minima
- The position of the n-th maximum from the central maximum is given by:
\[ y_n = n \beta \]
- The position of the m-th minimum is given by:
\[ y_m = \left(m - \frac{1}{2}\right) \beta \]

### Step 4: Calculate the position of the 3rd maximum
For the 3rd maximum (n = 3):
\[ y_3 = 3 \beta = 3 \times 0.5 \text{ mm} = 1.5 \text{ mm} \]

### Step 5: Calculate the position of the 2nd minimum
For the 2nd minimum (m = 2):
\[ y_2 = \left(2 - \frac{1}{2}\right) \beta = \left(1.5\right) \beta = 1.5 \text{ mm} \]

### Step 6: Calculate the distance between the 3rd maximum and the 2nd minimum
Since the 3rd maximum is on one side of the central maximum and the 2nd minimum is on the opposite side, the total distance (Δx) between them is:
\[ \Delta x = y_3 + y_2 = 1.5 \text{ mm} + 1.5 \text{ mm} = 3.0 \text{ mm} \]

### Final Answer
The distance of the 3rd maxima from the 2nd minima on the other side of the central maxima is **3.0 mm**.

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