If the wavelength of light used in a diffraction experiment is halved, what happ
Practice Questions
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
Questions & Step-by-Step Solutions
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?
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.
Diffraction and Wavelength Relationship – The relationship between wavelength and the angular position of minima in a single-slit diffraction pattern, where the position of minima is directly proportional to the wavelength.
