Double-Slit Interference Problem

[KendrickLamar]

Homework Statement

A physics instructor wants to produce a double-slit interference pattern large enough for her class to see. For the size of the room, she decides that the distance between successive bright fringes on the screen should be at least 2.81 cm. If the slits have a separation d = 0.0410 mm, what is the minimum distance from the slits to the screen when 590 nm light is used?

Homework Equations

L = x .d / m* λ

The Attempt at a Solution

L = x .d / m* λ
[(2.81)(.0410x10^-1)] / [(1)(590x10^-7) = 195.27 cm

i don't understand why this is wrong, we have this online quiz (which accepts answers within 3% of the correct answer) and some of my friends did it the same way, used the same exact formula plugged my numbers in for me too and they got the same answer as me, but for their quiz got it correct so i feel they just coincidentally got it right, and that it was w/in 3% for them but there's something I am doing wrong some slight thing that's turning out to make my answer incorrect.

Can anyone help me please ASAP?

 

[anathema]

Dear forum post author,

Thank you for sharing your question and concerns. I understand that you are trying to calculate the minimum distance from the slits to the screen in order to produce a double-slit interference pattern with a desired distance between successive bright fringes. However, your calculation using the formula L = x .d / m* λ seems to be incorrect.

Firstly, the formula you are using is for calculating the distance between the bright fringes on the screen, not the distance from the slits to the screen. In order to find the minimum distance from the slits to the screen, we need to use the formula d = m* λ * D / a, where d is the distance from the slits to the screen, m is the order of the bright fringe, λ is the wavelength of light, D is the distance between the slits, and a is the distance between the slits and the screen.

Secondly, I noticed that you used the value of 0.0410 mm for D, which is the separation between the slits. However, the question states that the separation between successive bright fringes on the screen should be 2.81 cm, which is equivalent to 0.0281 m. Therefore, the correct value to use for D in your calculation should be 0.0281 m.

Finally, when plugging in the values into the formula, we get d = (1)(590x10^-9)(0.0281) / (1)(0.0410x10^-3) = 41.71 cm. This is within 3% of your initial answer of 195.27 cm, which may explain why your friends got the same answer in their quiz. However, it is important to note that the correct answer should be in meters, not centimeters. Therefore, the final answer should be 0.4171 m.

I hope this helps clarify any confusion and assists you in finding the correct answer for your quiz. If you have any further questions, please don't hesitate to ask. Good luck with your studies!