In a double-slit experiment, if the wavelength of light is halved, what happens

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Question: In a double-slit experiment, if the wavelength of light is halved, what happens to the fringe width? (2020)

Options:

Correct Answer: It doubles

Exam Year: 2020

Solution:

Fringe width (β) is given by β = λD/d. If λ is halved, β will also be halved.

In a double-slit experiment, if the wavelength of light is halved, what happens to the fringe width? (2020)

In a double-slit experiment, if the wavelength of light is halved, what happens to the fringe width? (2020)

Step 1: Understand the double-slit experiment. It involves light passing through two slits and creating a pattern of bright and dark spots called fringes.
Step 2: Know the formula for fringe width (β), which is β = λD/d, where λ is the wavelength of light, D is the distance from the slits to the screen, and d is the distance between the slits.
Step 3: Identify what happens when the wavelength (λ) is halved. If λ becomes λ/2, we need to see how this affects β.
Step 4: Substitute the new wavelength into the formula: β = (λ/2)D/d.
Step 5: Simplify the equation: β = (1/2)(λD/d) = (1/2)β_initial, where β_initial is the original fringe width.
Step 6: Conclude that if the wavelength is halved, the fringe width will also be halved.

Double-slit experiment – A fundamental experiment in wave optics demonstrating the wave nature of light through interference patterns.
Fringe width – The distance between adjacent bright or dark fringes in an interference pattern, dependent on wavelength, distance to the screen, and slit separation.
Wavelength effect – Understanding how changes in wavelength affect the interference pattern, specifically the fringe width.