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

To find the width of the central fringe in a single-slit diffraction pattern, you can use the formula for the width of the central maximum: \[ W = \frac{2 \cdot \lambda \cdot L}{a} \] Where: - \( W \) is the width of the central maxima, - \( \lambda \) is the wavelength of the light (440 nm or \( 440 \times 10^{-9} \) m), - \( L \) is the distance to the screen (2.5 m), - \( a \) is the width of the slit (0.4 mm or \( 0.4 \times 10^{-3} \) m). Plugging in these values: \[ W = \frac{2 \cdot 440 \times 10^{-9} \cdot 2.5}{0.4 \times 10^{-3}} \] Calculating this gives: \[ W = \frac{2 \cdot 440 \cdot 2.5}{0.4} \times 10^{-6} \] \[ = \frac{2200}{0.4} \times 10^{-6} \] \[ = 5500 \times 10^{-6} \] \[ = 0.0055 \text{ m} \] So the width of the central fringe is approximately 5.5 mm. Isn’t it fascinating how even a simple experiment with light can lead us to such intriguing patterns? The physics of single-slit diffraction not only showcases how light behaves but also opens doors to understanding wave-particle duality! Now, if you ever find yourself staring at those patterns and wondering why they look so mesmerizing, just remember that it’s all about the way light interacts with edges and openings. Playing around with different slit widths can reveal even more about the dance of light!