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Const@ntine
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Homework Statement
https://attachment.outlook.office.net/owa/psaraskostas@hotmail.com/service.svc/s/GetFileAttachment?id=AQMkADAwATYwMAItYWVhZi1kMjdjLTAwAi0wMAoARgAAA5PfTv0SpppHr3yc003kVrgHAAH04A%2BJ7mRGmo%2BChKo3rFcAAAIBDAAAAAH04A%2BJ7mRGmo%2BChKo3rFcAAADhQYzEAAAAARIAEABF9QJlkOpsQ7K16ghu%2FR4q&X-OWA-CANARY=bC9TQBru00KIAJfDrF7wOUA-v2MS5tQYcRcIDvCJVDVpfrxruNXN3shXZtBC7JI_1CrNLme5I60.&token=eyJ0eXAiOiJKV1QiLCJhbGciOiJSUzI1NiIsIng1dCI6ImVuaDlCSnJWUFU1aWpWMXFqWmpWLWZMMmJjbyJ9.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.e0JhGUznvcXpY5TcsOa_djRRybR7Uqjm66-5hbtGqnWG4V6KcwaibG_1ssNOPvI4Af73Lryh1vIFiZvwlBhhYXIK3uqpb-4dcpFcMlhjymi3OxUlHc2Do7gz-vZRqbnN-FZV51vZpqfumhhhRorE6d1ndIoEjo4jexpbG8Q29Oq-9D-pwlUZPbSTlt4_7Vflyx19FoC0MJwbVId0LValKK3Qg4fXPsqed_wAk28cMKSN3IeNctKg5NBrvFgx-9mxmLrybMAbRL-AYZSuBLmV7hGmENa3oqdOGm3Z46fZZkDBvtBLK52ATd0n5aEzLOt0GMHxxpPCQYV4xFZOnAgScw&owa=outlook.live.com&isc=1&isImagePreview=True The lens and the reflector have a distance of d = 1.00 m between them. They have a focal length (f) of +80.0 cm & -50.0 cm, respectively. An object is situated at p = 1.00 m left of the lens.
(a) What's the position of the final idol, which is created by light that has gone through the lens two times?
(b) Is the idol inverted or not?
Homework Equations
1/p + 1/q = 1/f
Signs:
>For Lenses:
p: + when the object is in front of the lens, - if it's behind
q: + when the idol is behind the lens, - if it's in the front
h': + when the idol is standing/not inverted, - if it's inverted
R1 & R2: + when the centre of curvature is behind the lens, - when it's behind the lens
f: + when the lens is convergent, - when the lens is divergent
>For Reflectors:
p: + when the object is in front of the reflector, - if it's behind
q: + when the idol is in front of the reflector, - if it's behind
h': + when the idol is standing/not inverted, - if it's inverted
f & R: + when the reflector is hollow, - when the reflector is curved
M: + when the idol is standing/not inverted, - when the idol is inverted
The Attempt at a Solution
Gotta be honest here, I've tried this about 3 times but I always screw up at the end. Anyway, let's take it from the beginning:
Lens:
1/p1 + 1/q1 = 1/f1 <=> 1/1m + 1/q1 = 1/0.8m <=> q1 = + 4.00 m [Behind the lens]
M1 = -q1/p1 = - 4 [Bigger than the object, inverted]
So now, the idol is 4 meters behind the lens. Therefore,now that the idol is acting like the object for the reflector, it's p2 should be 3.00 m (d + p2 = q1 <=> 1m + p2 = 4m <=> p2 = 3.00 m). It is, however, behind the reflector, so it should be p2 = - 3.00 m.
And that's where I get stuck. In my book, I have only two examples, one for curved, and one for hollow reflectors, and they're just the basic stuff. Now here, the reflector is curved, but since the idol/"new object" is facing the hollow side, shouldn't it work as a hollow reflector? I mean, I can just take the 1/p + 1/q = 1/f formula again, this time for the reflector, but I don't get the proper result.
1/p2 + 1/q2 = 1/f2 <=> 1/-3m + 1/q2 = 1/-0.5m <=> q1 = - 0.6 m
Now,according to the book and all, the final idol should be 0.6 meters "behind the reflector". Problem is, what's the "behind" here? For a curved reflector, it's behind the hollow side, but for a hollow reflector it's the curved side.
Plus, there's this whole "light that has gone through the lens two times" thing. What does it mean? The book's answer is "160 cm to the left of the lens".
Any help is appreciated!