# data[].attributes.body
Hello, could you clarify what physically Q and Q' are? I understand which objects they are the images of but don't understand how you would 'see' Q or how the images would appear to a viewer. Also I appreciate the cat content. Thank you :)

# data[].attributes.headline
Why is sinx ≈ x ≈ tanx in derivation for young's double slit equation? 

# data[].attributes.subject
Why is sinx ≈ x ≈ tanx in derivation for young's double slit equation? 

# data[].attributes.body
Is there a reason other than for simplification that another small angle approximation is used to equate the expressions for sin x and tan x instead of just using the pythagorean identity to equate these expressions? Is there a reason I'm missing that would invalidate this?

(by x I really mean theta, it's just easier to write x)

Thank you!

# data[].attributes.headline
Doppler Effect With a Moving Source and Listener

# data[].attributes.subject
Doppler Effect With a Moving Source and Listener

# data[].attributes.body
I'm having difficulty fully understanding how the following change can be applied generally:
Vs->Vs-VL
I understand how this change works when the source and listener are moving in the same direction, but am struggling to make sense of the sign on VL when the source and listener move in opposite directions, wouldn't Vs-> Vs+VL in this case?

# data[].attributes.body
Were there any changes that had to be made to Huygen's theory, as didn't he propose it with light as a longitudinal wave rather than transverse?

# data[].attributes.body
Does the light which is allowed through the polarizing filter get diffracted like how light is diffracted by a diffraction grating? The series of parallel wires in a polarizing filter seems very similar to a diffraction grating for me.

# data[].attributes.body
When deriving the full intensity pattern for the single slit in video 3 around 3 minutes the phasor arrows of the different segments are compared, the arrow at top has phase 0 and as we go down the arrows rotate anticlockwise, why is it anticlockwise and not clockwise?  The ray at the top has the longest path hence his phase should be the 'most advanced', shouldn't it? And the other arrows should lag behind the top arrow and be slightly rotated in the clockwise direction, where is my mistake?

# data[].attributes.headline
Mapping a transverse wave on to the longitudinal wave

# data[].attributes.subject
Mapping a transverse wave on to the longitudinal wave

# data[].attributes.body
In slide 9 where the compressions and rarefactions are overlayed with the sinusoidal wave, I was confused about the wave drawn as I would have thought the crests and troughs match the compression and rarefaction. I wanted to understand the shape of the curve. Thanks

# data[].attributes.body
As light's wavelength is in the order of hundreds of nanometres, wouldn't a tiny error in the distance between A and each mirror make a huge difference, as even 250nm might cause the phase difference to be an entire wavelength?

In that case, how can we assume that both distances are exactly equal? Was the original experiment done so that they expected a phase difference, and then checked, say, 3 months later to see if the phase difference was changed?

# data[].attributes.body
To derive the standing wave function we need to write down the wave function for an incoming wave and its reflection. The derivation only works if the reflected wave has undergone a phase shift of pi. Why does the reflected wave change phase? Thank you!

# data[].attributes.body
In part c of the worked examples on phase difference (the 2nd video) the question specifies that the second wave is at zero and rising. I thought this would mean pi/2 is not correct, but 3pi/2 is? I drew the phasors that just confirmed what I thought. I got the general answer to be 3pi/2 + 2kpi. Please could you explain how the other values work too? I would understand if it was negative pi/2. Thank you, Liz

# data[].attributes.body
I do not understand why the image is erect, should it not be like lecture slide 17 and be flipped?

# data[].attributes.body
Is the single slit diffraction 'envelope' over the interference patterns for more than one slit an approximation? My reasoning is: shouldn't the diffraction pattern for each slit have minima/ maxima in slightly different places as the slits themselves are in slightly different places?

# data[].attributes.headline
Solving for the nodes of a standing wave

# data[].attributes.subject
Solving for the nodes of a standing wave

# data[].attributes.body
Alex: A few people have asked why we didn't solve for sin(wt) = 0 to find the positions of the nodes. The reason for this is that, in this case, we're interested to find the points x for which the displacement is zero for all time. Thus, these are the values of x that make the displacement zero, regardless of the time t (in which case we can consider sin(wt) to be something that's possible non-zero). In this case this requires us to solve for x such that sin(kx) = 0 (referring to the example that we worked through during lecture 2)

# data[].attributes.body
I understand Huygens principle and how it can help us pick up how waves propagate, but not exactly how I'd use it in a question. In what way would we be expected to apply the principle, if not just as a way to understand waves?

# data[].attributes.body
Hi. The Object-Image Relations for spherical reflecting/refracting surfaces both relied on the paraxial approximations. However, if the light rays under consideration were at quite a large angle with respect to the Optic Axis, would it be possible to derive a (most likely fairly nasty) relationship between s and s' ?

# data[].attributes.body
All slits are a common distance apart doesn't imply that the angle between each slit uses m(lambda)=dsin(theta). So, is the need for the angle to be the same between all phasor arrows a consequence of a small angle approximation? Thank you!

# data[].attributes.body
I followed the derivation guide but it doesn't seem to follow all the way through to the end like in the book (I may have not understood well). Either way, from 15.18 to 15.19, how does the LHS become the second partial derivative as x approaches zero? Thanks!

# data[].attributes.headline
Destructive Inteference and Conservation of Momentum

# data[].attributes.subject
Destructive Inteference and Conservation of Momentum

# data[].attributes.body
How come 2 pulses with amplitudes A and -A travelling in opposite directions on a string (assuming no energy loss)  pass through each other rather than just cancelling out (which would also be possible by momentum conservation)?

# data[].attributes.body
Why is s' negative? shouldn't it be positive since it's on the same side as the reflecting ray.

# data[].attributes.body
What is the difference between v and v subscript y?

# data[].attributes.body
Hi there! Thanks for your question :)

I originally typed an answer to this then realised it was rubbish so I just recorded myself instead, I hope this helps :)

# data[].attributes.body
At around the 11 minute mark, the slide shows that I=4Ep^2 and we know that  Ep=2Ecos(phi/2)
Therefore wouldn't this mean that for intensity we would get I=4(2Ecos(phi/2)^2=16E^2cos^2(phi/2) and not just 4 as the coefficient in place of 16.
Thank you!

# data[].attributes.body
I am confused as to how standing waves can form in completely open and half-open pipes. What are the incoming sound wave

# data[].attributes.body
Hi, I can't for the life of me get my head around the refraction derivation and how to get to the final equation (na/s + nb/s' = nb - na/R). Is there any chance you could go through it?

# data[].attributes.body
I am confused as to how standing waves can form in completely open and half-open pipes. What are the incoming sound waves reflecting off? I understand that the incoming and reflected sound waves interfere  to produce the standing wave, but how is the incoming wave reflected if there is an 'open end', isn't there no boundary to reflect off?

# data[].attributes.body
Hey, I don't really understand the derivation of the lens maker's equation, mainly, why the image formed by the first surface of a lens serves as the object for the second surface? I don't see how this is acts as an object from the diagram

# data[].attributes.body
With the example considering the image of an extended object in a concave mirror, why is there only one s' if P' and Q' are at different distances from V?

# data[].attributes.body
How I can create a convex/concave lens on this app?

# data[].attributes.headline
Wave equation and power equation derivations

# data[].attributes.subject
Wave equation and power equation derivations

# data[].attributes.body
Are these two derivations included in the first waves and optics lecture examinable?

# data[].attributes.body
In the interpret section of the derivation guide you have asked the question "3. What if the radii of curvature of the lens are both the same, does this
mean that the focal length must be infinite?". I have tried to reason an answer to this question by looking at the equation and I think that if the radii are the same, the focal length is infinite, but this feels wrong intuitively. What is the correct answer to this question and could you explain why?