Astrophysics diffraction question
Hi, I've been stumped at this question as I don't really understand the mark scheme..
part b specifically, I've sketched the diagrams out and used the alternate angle theorem to show A next to d(A), but I have no idea what I can equate to get cosA. It says use trig but I don't know how to link the first situation with the second either.. the only formula for this topic is dsin(theta) = n(lambda)
Any explanations please give in quite simple terms please, thank you
part b specifically, I've sketched the diagrams out and used the alternate angle theorem to show A next to d(A), but I have no idea what I can equate to get cosA. It says use trig but I don't know how to link the first situation with the second either.. the only formula for this topic is dsin(theta) = n(lambda)
Any explanations please give in quite simple terms please, thank you
draw the first image titled like the second image with d and the 2 arrows next to d also tilted. d is the length between the 2 white gaps and this stays constant. therefore d is the hypotenuse. now draw dA underneath the tilted grating as a horizontal line. dA is the horizontal of the right angled triangle.
therefore dA (apparent D as written in the markscheme) = dcosA as adjacent = hypotenuse * cos(x)
therefore dA (apparent D as written in the markscheme) = dcosA as adjacent = hypotenuse * cos(x)
It's pure trig, the diffraction formula is not relevant here.
The same grating is used in both diagrams, just turned to a different angle to make the spacing look closer. You'd see the same thing if you looked at the safety fence near a pedestrian crossing from different angles as you rode your bike down the road past one.
In the second diagram is a right angle triangle hiding in plain sight. the hypotenuse is the real spacing of the grating d, the adjacent side is the apparent spacing da.
The same grating is used in both diagrams, just turned to a different angle to make the spacing look closer. You'd see the same thing if you looked at the safety fence near a pedestrian crossing from different angles as you rode your bike down the road past one.
In the second diagram is a right angle triangle hiding in plain sight. the hypotenuse is the real spacing of the grating d, the adjacent side is the apparent spacing da.
Original post by user8937264980
draw the first image titled like the second image with d and the 2 arrows next to d also tilted. d is the length between the 2 white gaps and this stays constant. therefore d is the hypotenuse. now draw dA underneath the tilted grating as a horizontal line. dA is the horizontal of the right angled triangle.
therefore dA (apparent D as written in the markscheme) = dcosA as adjacent = hypotenuse * cos(x)
therefore dA (apparent D as written in the markscheme) = dcosA as adjacent = hypotenuse * cos(x)
Ohh, I didn't think of doing it that way
Thank you very much that helps a lot
Original post by Joinedup
It's pure trig, the diffraction formula is not relevant here.
The same grating is used in both diagrams, just turned to a different angle to make the spacing look closer. You'd see the same thing if you looked at the safety fence near a pedestrian crossing from different angles as you rode your bike down the road past one.
In the second diagram is a right angle triangle hiding in plain sight. the hypotenuse is the real spacing of the grating d, the adjacent side is the apparent spacing da.
The same grating is used in both diagrams, just turned to a different angle to make the spacing look closer. You'd see the same thing if you looked at the safety fence near a pedestrian crossing from different angles as you rode your bike down the road past one.
In the second diagram is a right angle triangle hiding in plain sight. the hypotenuse is the real spacing of the grating d, the adjacent side is the apparent spacing da.
Thanks for the explanation, I didn't think of it that way!
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