In Young's double-slit experiment, if the distance between the slits is 0.2 mm and the distance to the screen is 1 m, what is the fringe width if the wavelength of light used is 500 nm?
Practice Questions
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Q1
In Young's double-slit experiment, if the distance between the slits is 0.2 mm and the distance to the screen is 1 m, what is the fringe width if the wavelength of light used is 500 nm?
0.1 mm
0.2 mm
0.5 mm
0.8 mm
Fringe width (β) = λD/d. Here, D = 1 m, d = 0.2 mm = 0.0002 m, λ = 500 nm = 500 x 10^-9 m. β = (500 x 10^-9 * 1) / 0.0002 = 0.0025 m = 0.25 mm.
Questions & Step-by-step Solutions
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Q
Q: In Young's double-slit experiment, if the distance between the slits is 0.2 mm and the distance to the screen is 1 m, what is the fringe width if the wavelength of light used is 500 nm?
Solution: Fringe width (β) = λD/d. Here, D = 1 m, d = 0.2 mm = 0.0002 m, λ = 500 nm = 500 x 10^-9 m. β = (500 x 10^-9 * 1) / 0.0002 = 0.0025 m = 0.25 mm.
Steps: 7
Step 1: Identify the given values from the problem. The distance between the slits (d) is 0.2 mm, the distance to the screen (D) is 1 m, and the wavelength of light (λ) is 500 nm.
Step 2: Convert the values to the same unit. Convert 0.2 mm to meters: 0.2 mm = 0.2 / 1000 = 0.0002 m. Convert 500 nm to meters: 500 nm = 500 x 10^-9 m.
Step 3: Write 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) / 0.0002 m.
Step 5: Calculate the numerator: 500 x 10^-9 m * 1 m = 500 x 10^-9 m.
Step 6: Calculate the fringe width: β = (500 x 10^-9) / (0.0002) = 0.0025 m.
Step 7: Convert the fringe width back to mm: 0.0025 m = 0.0025 * 1000 = 2.5 mm.
