Question 14
Saffron light has a wavelength of 440 nm, It shines through a single sift 0.4 mm wide,
If a screen is 2.5 m away, how WIDE is the central fringe (from lower dark fringe to
higher dark fringe)?
2

Question

UpStudy AI · Accepted Answer

To determine the width of the central fringe in a single-slit diffraction pattern, we'll use the following information:

- **Wavelength (λ):** 440 nm = $$ 440 \times 10^{-9} $$ meters
- **Slit width (a):** 0.4 mm = $$ 0.4 \times 10^{-3} $$ meters
- **Distance to screen (D):** 2.5 meters

### Step 1: Find the Position of the First Dark Fringe

In single-slit diffraction, the position of the first dark fringe ($$ y $$) on either side of the central maximum is given by:

$$
a \sin \theta = m \lambda
$$

For the first dark fringe, $$ m = 1 $$. Assuming the small angle approximation ($$ \sin \theta \approx \tan \theta \approx \frac{y}{D} $$), we can rewrite the equation as:

$$
y = \frac{m \lambda D}{a}
$$

Plugging in the values:

$$
y = \frac{1 \times 440 \times 10^{-9} \, \text{m} \times 2.5 \, \text{m}}{0.4 \times 10^{-3} \, \text{m}} = \frac{1.1 \times 10^{-6}}{0.4 \times 10^{-3}} = 2.75 \times 10^{-3} \, \text{m} = 2.75 \, \text{mm}
$$

### Step 2: Calculate the Total Width of the Central Fringe

The central fringe spans from the first dark fringe on one side to the first dark fringe on the opposite side. Therefore, the total width ($$ W $$) is:

$$
W = 2y = 2 \times 2.75 \, \text{mm} = 5.5 \, \text{mm}
$$

### **Final Answer:**
The central fringe is approximately 5.5 millimeters wide.
The central fringe is about 5.5 millimeters wide.

Question 14
Saffron light has a wavelength of 440 nm, It shines through a single sift 0.4 mm wide,
If a screen is 2.5 m away, how WIDE is the central fringe (from lower dark fringe to
higher dark fringe)?
2

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Question 14 Saffron light has a wavelength of 440 nm, It shines through a single sift 0.4 mm wide, If a screen is 2.5 m away, how WIDE is the central fringe (from lower dark fringe to higher dark fringe)? 2

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The Deep Dive

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Latest Physics Questions

Question 14
Saffron light has a wavelength of 440 nm, It shines through a single sift 0.4 mm wide,
If a screen is 2.5 m away, how WIDE is the central fringe (from lower dark fringe to
higher dark fringe)?
2