What is the fringe width in a double-slit experiment if the wavelength of light
Practice Questions
Q1
What is the fringe width in a double-slit experiment if the wavelength of light is 500 nm, the distance between the slits is 0.2 mm, and the distance to the screen is 1 m?
0.5 mm
1 mm
2 mm
0.25 mm
Questions & Step-by-Step Solutions
What is the fringe width in a double-slit experiment if the wavelength of light is 500 nm, the distance between the slits is 0.2 mm, and the distance to the screen is 1 m?
Step 1: Identify the given values from the problem. The wavelength of light (λ) is 500 nm, the distance between the slits (d) is 0.2 mm, and the distance to the screen (D) is 1 m.
Step 2: Convert the units to meters for consistency. 500 nm = 500 x 10^-9 m and 0.2 mm = 0.2 x 10^-3 m.
Step 3: Write down the formula for fringe width (β): β = λD/d.
Step 4: Substitute the values into the formula: β = (500 x 10^-9 m)(1 m) / (0.2 x 10^-3 m).
Step 5: Calculate the numerator: 500 x 10^-9 m * 1 m = 500 x 10^-9 m.
Step 6: Calculate the denominator: 0.2 x 10^-3 m = 0.0002 m.
Step 7: Divide the numerator by the denominator: β = (500 x 10^-9 m) / (0.0002 m).
Step 8: Perform the division: β = 2.5 x 10^-3 m = 2.5 mm.
