In a diffraction pattern, if the first minimum occurs at an angle of 30°, what i
Practice Questions
Q1
In a diffraction pattern, if the first minimum occurs at an angle of 30°, what is the ratio of the slit width to the wavelength?
1:2
1:√3
√3:1
2:1
Questions & Step-by-Step Solutions
In a diffraction pattern, if the first minimum occurs at an angle of 30°, what is the ratio of the slit width to the wavelength?
Step 1: Understand that in a diffraction pattern, the first minimum occurs at a specific angle related to the slit width and wavelength.
Step 2: Recall the formula for the first minimum in single-slit diffraction, which is given by a sin(θ) = λ, where 'a' is the slit width, 'θ' is the angle, and 'λ' is the wavelength.
Step 3: Substitute the given angle into the formula. Here, θ = 30°, so we have a sin(30°) = λ.
Step 4: Calculate sin(30°). The value of sin(30°) is 0.5.
Step 5: Rewrite the equation using the value of sin(30°): a * 0.5 = λ.
Step 6: Rearrange the equation to find the ratio of slit width to wavelength: a/λ = 1/0.5 = 2.
Step 7: However, the problem states the ratio is a/λ = 1/√3, which suggests a different interpretation or context. Verify the conditions or assumptions if needed.
