Can a Diffraction Pattern be Solved Without Complete Information?

[David Truong]

Homework Statement

A single slit illuminated by light of wavelength λ = 610 nm produces a diffraction pattern with its first minimum at 3.5 mm from the central maximum. (a) Find the slit width, and (b) For the same slit, what wavelength of light would produce a first minimum at θ = 4.0 degrees.

Homework Equations

D = slit width
m = minima order
L = distance from the slit to the wall

D sin θ = m λ
tan θ = sin θ = θ (small angle approximation)

The Attempt at a Solution

λ = 610 nm or 6.1 x 10^-7 m
m = 1 (first order minima)
x = 3.5 mm (which is the distance from the central maximum to the first minimum)

tan θ = x / L

D = m λ / sin θ

I would be able to solve this question if I was given either the distance from the slit to the wall (L) or the angle (θ), however, I am not given any of this, and as such, I am unsure how to proceed.

 

[Simon Bridge]

It is not possible to solve the problem with the information written above.
You should complain to the person who set the problem - make sure you have read all the information given as sometimes a vital bit is someplace else. Check with other people doing the same problem - it helps to have others also complaining.

 

[DrPapper]

Hello David,

Please update us if the professor says it was right and then shows you how to do it. I've been thinking about this question for a bit but have not come up with a solution for you. I agree with Simon, I do not believe it can be solved as presented. But I will think about it more if I have time later this week. Please keep us updated. In the mean time don't get too caught up on it. Move on to other problems. :D

Best Regards,

Caleb P.