Figure EX33.26 shows the light intensity on a screen behind a single slit. The wavelength of the light is 600 nm and the slit width is 0.15 mm. What is the distance from the slit to the screen?

Verified step by step guidance

1. Step 1: Understand the problem. The question involves a single-slit diffraction pattern, where the light intensity distribution is shown on the screen. The goal is to calculate the distance from the slit to the screen using the given wavelength (600 nm), slit width (0.15 mm), and the diffraction pattern.
2. Step 2: Recall the formula for single-slit diffraction. The angular position of the minima in the diffraction pattern is given by: $m\lambda \; =\; a\; sin\; \theta$, where m is the order of the minima, λ is the wavelength, a is the slit width, and θ is the angle of diffraction.
3. Step 3: Relate the angular position to the physical distance on the screen. The distance from the central maximum to the first minimum on the screen (x) is related to the angle θ by: $tan\; \theta \; =\; x\; /\; L$, where L is the distance from the slit to the screen. For small angles, $sin\; \theta \; \approx \; tan\; \theta \; \approx \; x\; /\; L$.
4. Step 4: Use the given data to find x. From the graph, the distance between the central maximum and the first minimum is approximately 0.5 cm (or 0.005 m). Substitute this value into the small-angle approximation: $sin\; \theta \; \approx \; x\; /\; L$.
5. Step 5: Solve for L. Combine the equations: $m\lambda \; =\; a\; (x\; /\; L)$. For the first minimum (m = 1), rearrange to find L: $L\; =\; a\; x\; /\; \lambda$. Substitute the values: a = 0.15 mm = 0.00015 m, x = 0.005 m, and λ = 600 nm = 6 × 10^-7 m.

Key Concepts

Single Slit Diffraction

Single slit diffraction occurs when light passes through a narrow opening, causing it to spread out and create a pattern of light and dark fringes on a screen. The width of the slit and the wavelength of the light determine the characteristics of the diffraction pattern, including the position and intensity of the maxima and minima.

Wavelength and Frequency

Wavelength is the distance between successive peaks of a wave, while frequency is the number of waves that pass a point in one second. In the context of light, the wavelength determines the color of the light and influences the diffraction pattern produced when light interacts with obstacles, such as a slit.

Intensity Distribution

The intensity distribution in a diffraction pattern describes how the brightness of light varies across the screen. It is typically highest at the center and decreases towards the edges, forming a series of alternating bright and dark regions. This distribution is influenced by the slit width, wavelength, and distance from the slit to the screen.