Chapter 2, Problem 8Q

Consider a image that is located 30 cm in front of a lens. It forms an upright image 7.5 cm from the lens. Theillumination is so bright that that a faint inverted image, due to reflection off the front of the lens, is observedat 6.0 cm on the incident side of the lens. The lens is then turned around. Then it is observed that the faint,inverted image is now 10 cm on the incident side of the lens.What is the index of refraction of the lens?

2. In class, we discussed several different flow scenarios for which we can make enough assumptions to simplify the Navier-Stokes equations enough to solve them and obtain an exact solution. Consulting the cylindrical form of the Navier-Stokes equations copied below, please answer the following questions. др a 1 a + +0x- + +O₂ = Pgr + μl 18²v, 2 ave ²v₁] az2 + at or r de r Əz dr ar Vodvz др [18 + + +Or + +Vz = Pgz +fl at ar r 20 ôz ôz dr ave дов V,Ve ave +Or + + = pge at dr r 80 Əz + az2 a.) In class, we discussed how the Navier-Stokes equations are an embodiment of Newton's 2nd law, F = ma (where bolded terms are vectors). Name the 3 forces that we are considering in our analysis of fluid flow for this class. др a 10 1 ve 2 av 2200] + +μ or 42 30 b.) If we make the assumption that flow is "fully developed" in the z direction, which term(s) would go to zero? Write the term below, describe what the term means in simple language (i.e. do not simply state "it is the derivative of a with…

1. Consult the form of the x-direction Navier-Stokes equation below that we discussed in class. (For this problem, only the x direction equation is shown for simplicity). Note that the equation provided is for a Cartesian coordinate system. In the spaces below, indicate which of the following assumptions would allow you to eliminate a term from the equation. If one of the assumptions provided would not allow you to eliminate a particular term, write "none" in the space provided. du ди at ( + + + 매일) du ди = - Pgx dy др dx ²u Fu u + fl + ax2 ay² az2 - дх - Əz 1 2 3 4 5 6 7 8 9 Assumption Flow is in the horizontal direction (e.g. patient lying on hospital bed) Flow is unidirectional in the x-direction Steady flow We consider the flow to be between two flat, infinitely wide plates There is no pressure gradient Flow is axisymmetric Term(s) in equation