Need Help Solving Physics Problem Regarding Green Light

[tgoot84]

hey so I'm having a lot of trouble on this section of physics.
the question I'm on is:
Green light (546nm) strikes a single slit at normal incidence. what width slit will produce a central maximum that is 2.3 cm wide on a screen 1.42m from the slit?

I've been trying to manipulate Wsin(0)=wavelength and y=Ltan(O), but i can't get anything to work.

I appreciate any help.

 

[barob1n]

I thought maybe I could help, but my physics textbook exploded while I was looking into the details surrounding this question. True story.

 

[kyle8921]

Hello there,

It seems like you are on the right track in using the equations Wsin(θ)=λ and y=Ltan(θ) to solve this problem. In order to find the width of the slit, you will need to rearrange these equations to solve for W.

First, let's start with the equation Wsin(θ)=λ. We know that the wavelength (λ) is given as 546 nm, or 5.46 x 10^-7 m. We also know that the angle of incidence (θ) is 0 degrees since the light is hitting the slit at normal incidence. Therefore, we can simplify the equation to Wsin(0)=5.46 x 10^-7 m.

Since sin(0)=0, this means that W x 0 = 5.46 x 10^-7 m. This means that the width of the slit (W) must be 0 in order to produce a central maximum that is 2.3 cm wide on the screen. This does not seem to make sense, so let's try using the second equation, y=Ltan(θ).

We know that the distance from the slit to the screen (L) is given as 1.42 m. We also know that the angle of incidence (θ) is 0 degrees. Therefore, the equation becomes y=1.42 x tan(0).

Since tan(0)=0, this means that y=0. This also does not make sense since the central maximum is supposed to be 2.3 cm wide on the screen.

After reviewing the equations and given values, it seems like there may be a mistake in the question or the given values. The width of the slit cannot be 0 in order to produce a central maximum on the screen. I would recommend double-checking the question and values given, and if you are still having trouble, consult with your teacher or a classmate for further assistance. Keep up the good work in tackling this challenging physics problem!