Combining Lenses and Mirrors: Finding the Focal Length and Image Formation

AI Thread Summary
The discussion centers on the focal length in a combination of lenses and mirrors, specifically questioning the use of a focal length of 15.0 cm instead of infinity for a plane mirror. It emphasizes the method of finding the first image formed by the front lens or mirror, which then serves as the object for subsequent optical elements. The process involves rays refracting through the lens, reflecting off the mirror, and refracting again through the lens to form a second image. It is noted that during the second refraction, the virtual image created by the mirror is treated as the object, leading to a negative object distance. The conversation seeks clarification on the correct approach to image formation in this optical setup.
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Homework Statement



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Question B only

Homework Equations





The Attempt at a Solution



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1) Why we use f=15.0cm? Shouldn't it be f=infinity considering plane mirror have an infinity focal length?
2) Normally I do combination(lens, mirrors), firstly I will consider the front lens/mirror by finding the 1st image formed. Then the 1st image will be the object of the subsequent lens/mirror. Am I using the right method to do?
 

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Rays from the object first refract through the lens, reflect from the mirror and then again refract though the lens to from I2. During the second refraction, the object is the vertual image I1 formed by the mirror. After refection from the mirror the rays appear to be converging at a distance equal to the distance of I1 behind the mirror. Hence u is negative.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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