Single Slit Diffraction Solved Examples
Example 1: A single-slit diffraction experiment uses light of wavelength λ = 600 nm and a slit width of a = 0.1 mm. Calculate the angular position (in degrees) of the first minimum.
Solution:
a = 0.1 mm = 0.1 × 10(-3) m
λ = 600 nm = 600 × 10(-9) m
For the first minimum, n = 1
Formula for the angular position of the first minimum: sin(θ) = n λ / a
Substituting values: sin(θ) = (1) × (600 × 10(-9)) / (0.1 × 10(-3))
Calculating: sin(θ) ≈ 0.006
Hence, θ ≈ 0.6 degrees
Example 2: In a single-slit diffraction experiment, light of wavelength λ = 500 nm produces the first minimum at an angle x = 0.04 cm from the central maximum. Determine the slit width (in mm).
Solution:
Given:
λ = 500 nm = 500 × 10-9m
x = 0.04 cm = 0.04 × 10-2 m
For the first minimum, n = 1
Formula for slit width: a = n × λ × x / sin(θ)
sin(θ) = x / D (D is the distance between the slit and the screen)
Substituting : a = (1) × (500 × 10(-9)) × (0.04 × 10-2 )/ (sin(θ))
Sin(θ) ≈ θ (for small angles), therefore a ≈ 5 × 10-3 m or 0.05 mm
Example 3. Light of wavelength λ = 500 nm passes through a slit of width a = 0.1 mm, creating a diffraction pattern on a screen. If the first minimum is observed at a distance x = 5 mm from the central maximum, what is the distance (in mm) between the screen and the slit?
Solution:
Given:
λ = 500 nm = 500 × 10-9m
a = 0.1 mm = 0.1 × 10-3m
x = 5 mm = 5 × 10-3m
For the first minimum, n = 1
Formula for distance: D = n λ x / a
Substituting values: D = (1) × (500 × 10-9) × (5 × 10-3) / (0.1 × 10-3)
D ≈ 6.4 mm
Example 4. For a single-slit diffraction pattern, light of wavelength λ = 500 nm produces the first minimum at an angular separation of Δθ = 60 degrees. Calculate the slit width (in mm).
Solution:
λ = 500 nm = 500 × 10-9m
Δθ = 60 degrees
For the central maximum, n = 1
Formula for slit width: a = n × λ / sin(Δθ)
Substituting values: a = (1) × (500 × 10-9) / sin(60 degrees)
Calculating: a ≈ 3.33 × 10-3m or 0.033 mm
Example 5: A monochromatic light of wavelength λ = 600 nm passes through a single slit and produces a diffraction pattern on a screen. If the angular width of the central maximum is 10 degrees, determine the width of the slit.
Solution:
Given:
Wavelength (λ) = 600 nm = 600 × 10-9 m
Angular width of the central maximum = 10 degrees
For the central maximum, n = 1
Formula for the width of the slit: a = n × λ / sin(Δθ)
Substituting values:
a = (1) × (600 × 10-9) / sin(10 degrees)
Calculating:
a ≈ 3.47 × 10-5 m or 34.7 μm
Single Slit Diffraction
Single Slit Diffraction is a fundamental concept in wave optics that explains how light behaves as a wave when passing through a narrow slit. When coherent light (like a laser) goes through a single narrow slit, the waves spread out, and their interaction creates a pattern on a screen placed some distance away. This phenomenon, known as diffraction, leads to the formation of alternating bright and dark regions, showcasing the wave nature of light.
In this article, we’ll learn core concepts, types, and practical applications of Single Slit Diffraction, aiming to simplify and explore its patterns and formulas.
Table of Content
- What is Single Slit Diffraction?
- Central Maximum
- Path Difference
- Minima Position
- Intensity Distribution Curve (Pattern)
- Single Slit Diffraction Formula
Diffraction is defined as the phenomenon in which light bends around the corners of an obstacle whose size is comparable to the wavelength of the light
Contact Us