A narrow slit of width 1 mm is illuminated by monochromatic light of wavelength 600 nm. The distance between the first minima on either side of a screen at a distance of 2 m is

Options

A. 1.2 cm
B. 1.2 mm
C. 2.4 cm
D. 2.4 mm

Answer

To solve the problem of finding the distance between the first minima on either side of a screen illuminated by monochromatic light through a narrow slit, we can follow these steps:

### Step 1: Identify the given values
- Width of the slit (d) = 1 mm = \(1 \times 10^{-3}\) m
- Wavelength of light (λ) = 600 nm = \(600 \times 10^{-9}\) m
- Distance from the slit to the screen (D) = 2 m

### Step 2: Understand the diffraction pattern
When light passes through a narrow slit, it creates a diffraction pattern on the screen. The positions of the minima can be calculated using the formula for single-slit diffraction.

### Step 3: Use the formula for minima in single-slit diffraction
The position of the first minima on either side of the central maximum is given by the formula:
\[ y = \frac{m \lambda D}{d} \]
where:
- \(y\) is the distance from the central maximum to the m-th minima,
- \(m\) is the order of the minima (for the first minima, \(m = 1\)),
- \(D\) is the distance from the slit to the screen,
- \(d\) is the width of the slit.

### Step 4: Calculate the distance for the first minima
For the first minima (\(m = 1\)):
\[ y = \frac{1 \cdot \lambda D}{d} = \frac{600 \times 10^{-9} \cdot 2}{1 \times 10^{-3}} \]
Calculating this gives:
\[ y = \frac{600 \times 10^{-9} \cdot 2}{1 \times 10^{-3}} = \frac{1200 \times 10^{-9}}{10^{-3}} = 1200 \times 10^{-6} \text{ m} = 1.2 \text{ mm} \]

### Step 5: Calculate the total distance between the first minima on either side
Since we want the distance between the first minima on either side of the central maximum, we need to double the value of \(y\):
\[ \text{Total distance} = 2y = 2 \cdot 1.2 \text{ mm} = 2.4 \text{ mm} \]

### Final Answer
The distance between the first minima on either side of the screen is **2.4 mm**.

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