In a double-slit experiment, if the distance between the slits is doubled while keeping the wavelength constant, what happens to the fringe width?
Practice Questions
1 question
Q1
In a double-slit experiment, if the distance between the slits is doubled while keeping the wavelength constant, what happens to the fringe width?
Doubles
Halves
Remains the same
Quadruples
Fringe width (β) is given by β = λD/d, where d is the distance between the slits. If d is doubled, β is halved.
Questions & Step-by-step Solutions
1 item
Q
Q: In a double-slit experiment, if the distance between the slits is doubled while keeping the wavelength constant, what happens to the fringe width?
Solution: Fringe width (β) is given by β = λD/d, where d is the distance between the slits. If d is doubled, β is halved.
Steps: 7
Step 1: Understand the formula for fringe width, which is β = λD/d.
Step 2: Identify the variables in the formula: λ is the wavelength, D is the distance from the slits to the screen, and d is the distance between the slits.
Step 3: Note that in this scenario, the wavelength (λ) and the distance to the screen (D) remain constant.
Step 4: Recognize that if the distance between the slits (d) is doubled, we replace d with 2d in the formula.
Step 5: Substitute into the formula: β = λD/(2d).
Step 6: Compare the new fringe width (β) with the original fringe width (β = λD/d).
Step 7: Since β = λD/(2d) is half of β = λD/d, we conclude that the new fringe width is half of the original fringe width.
