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Writer's picturekeshprad

Barron's 2nd Edition PT1 Q62


62) This question goes over Young's double-slit experiment and asks us which answer choice(s) will decrease the spacing between bright regions.

Where d is the distance between slits, y is the distance between bright regions, and L is the distance between the slits and the screen

The distance between bright fringes can be expressed with the following equation.

Where y is the distance between bright regions, m is the fringe number, λ is the wavelength, L is the distance between the slits and the screen, and d is the distance between slits

 

Choice A: By using a shorter wavelength, λ is decreased. For example, let's say that the wavelength λ is halved.

Where y is the distance between bright regions, m is the fringe number, λ is the wavelength, L is the distance between the slits and the screen, and d is the distance between slits

When the wavelength is halved, the distance between bright regions would be halved as well. Choice A is valid.


 

Choice B: Let's take an example where the distance from the slits to the screen is halved.

Where y is the distance between bright regions, m is the fringe number, λ is the wavelength, L is the distance between the slits and the screen, and d is the distance between slits

When the distance from the slits to the screen is halved, the distance between bright regions must be halved, in order to balance the equation. Choice B must be valid as well.


 

Choice C: Again let's take an example where we double the distance between the slits.

Where y is the distance between bright regions, m is the fringe number, λ is the wavelength, L is the distance between the slits and the screen, and d is the distance between slits

This shows us that if the distance between the slits is doubled, the distance between bright regions would be halved. Therefore, Choice C must also be valid.


 

Choice D: If we perform the experiment underwater, the speed of light will be slower due to the change to a denser medium. Using the wave equation v = f * λ we know that when the velocity decreases, so will the wavelength. As shown in the explanation of choice A, a shorter wavelength leads to a shorter distance between fringes. Choice D is valid.


 

All the choices will decrease the distance between the bright regions, so our answer is Choice E.


Answer: E

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