In a diffraction pattern, if the first minimum occurs at an angle of 30°, what i

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Question: 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?

Options:

Correct Answer: 1:√3

Solution:

Using the condition for the first minimum a sin(30°) = λ, we find the ratio a/λ = 1/√3.

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?

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.

Diffraction and Interference – Understanding the conditions for minima in a single-slit diffraction pattern, specifically using the formula a sin(θ) = nλ, where n is the order of the minimum.
Trigonometric Functions – Applying the sine function to find the angle corresponding to the first minimum in a diffraction pattern.