A level physics single slit diffraction with white light

Guys on the mark schemes it says that all the subsidiary maxima are half the central width which implies all the subsidiary maxima have the same fringe width but on the savemyexams notes it says the fringe width decreases further away from the centre and merges together. Which is it?

Reply 1

Ferret!

~~The latter (save my exams) is right for single-slit only (albeit, they have exaggerated the subsidiary maxima slightly).~~
Intensity follows the relation

I = I_{0} \frac {\sin^{2}(\beta)} {\beta^{2}}

, where

\beta=(\frac{ka}{2})\sin(\theta)

k

is the wavenumber,

a

is the width of the slit,

\theta

is the angle from the normal line from the centre of the slit to a point on the screen and

I_{0}

is the central maxima's intensity. See https://www.desmos.com/calculator/lejiayxjok .

(edited 11 months ago)

Reply 2

Eimmanuel

Study Forum Helper

Original post by Gcsestudent56

I would agree with the MS and it can be shown by the desmos plot produced by Ferret!(it seems that Ferret! does not know the desmos plot actually provides the evidence that MS is good and savemyexams notes is wrong)

We can obtain the roots of the function as shown below (the dots are the roots).

The following diagram also shows similar results.

Reply 3

Ferret!

Yeah, you are right Eimmanuel. I misread the question as for the subsidiary maxima's intensities rather than for their widths. Thanks for the correction, mistakes happen! :biggrin:

It seems savemyexams is also right, as they write:
The features of the single slit diffraction pattern are:

•

Subsidiary... half the width of the central maximum.

from https://www.savemyexams.com/a-level/physics/aqa/17/revision-notes/3-waves/3-4-diffraction/3-4-1-single-slit-diffraction/.

(edited 11 months ago)

Reply 4

JustBenjamin

Original post by eimmanuel

I would agree with the MS and it can be shown by the desmos plot produced by Ferret!(it seems that Ferret! does not know the desmos plot actually provides the evidence that MS is good and savemyexams notes is wrong)
We can obtain the roots of the function as shown below (the dots are the roots).

The following diagram also shows similar results.

Issue is that this is not what happens if the light isn't of a single wavelength, in reality each colour / wavelength will bend slightly differently, resulting in a pattern as seen below; which is what I believe they were referring to in terms of merging

(edited 11 months ago)

Reply 5

Eimmanuel

Study Forum Helper

Original post by JustBenjamin

At A level, exam boards tend to simplify the understanding of this ("this" means white light through single-slit) based on a "single wavelength pattern" as they would not want to complicate the story.

The description provided by savemyexams isn’t accurate too as we cannot use the definition of the fringe width from a single wavelength pattern... And I would stop here.

(edited 11 months ago)

Reply 6

JustBenjamin

Original post by eimmanuel

At A level, exam boards tend to simplify the understanding of this based on single wavelength pattern as they would not want to complicate the story.
The description provided by savemyexams isn’t accurate too as we cannot use the definition of the fringe width from a single wavelength pattern... And I would stop here.

The multi wavelength look comes from what we were thought in a level for the AQA spec. I just had a look at the spec and it specifically states that students are supposed to be aware of monochromatic vs white light differences with single slit diffraction, so while the savemy mark scheme isn’t correct, neither Is the a level one unless OP does an exam board where this is not part of the spec.
Alternatively maybe the question stated the light passes through a monochromatic filter or such but hard to say without knowing the question.