If the wavelength of light used in a diffraction experiment is halved, what happens to the angular position of the first minimum in a single-slit diffraction pattern?
Practice Questions
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Q1
If the wavelength of light used in a diffraction experiment is halved, what happens to the angular position of the first minimum in a single-slit diffraction pattern?
It remains the same
It doubles
It halves
It quadruples
Halving the wavelength will halve the angle for the first minimum, as the position of minima is directly proportional to the wavelength.
Questions & Step-by-step Solutions
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Q
Q: If the wavelength of light used in a diffraction experiment is halved, what happens to the angular position of the first minimum in a single-slit diffraction pattern?
Solution: Halving the wavelength will halve the angle for the first minimum, as the position of minima is directly proportional to the wavelength.
Steps: 6
Step 1: Understand that in a single-slit diffraction pattern, the position of the minima (dark spots) is determined by the wavelength of light used.
Step 2: Recall the formula for the angular position of the first minimum in a single-slit diffraction pattern, which is given by the equation: sin(θ) = λ / a, where λ is the wavelength and a is the width of the slit.
Step 3: Note that if the wavelength (λ) is halved, the new wavelength becomes λ/2.
Step 4: Substitute the new wavelength into the formula: sin(θ') = (λ/2) / a, where θ' is the new angle for the first minimum.
Step 5: Since sin(θ) is directly proportional to λ, halving λ means that sin(θ') will also be halved, leading to a smaller angle θ'.
Step 6: Conclude that halving the wavelength results in halving the angle for the first minimum.
