Gaussian Beams (use green light (λ = 532 nm for wavelength) for calculations). Carry out the algebra to derive the effect of a lens of focal length, f, on an input Gaussian beam with flat wave-front (Ri = [infinity]) and beam waist ωi = ωo at the lens entrance. What are R(d) and w(d) for all distances, d, to the right of the lens? (Work out the details to obtain general results.)

The higher the astm grain-size number, the coarser the grain is. a)-true b)-false

Apipe with an outside diameter of 15 cm is exposed to an ambient air and surrounding temperature of -20°c. the pipe has an outer surface temperature of 65°c and an emissivity of 0.85. if the rate of heat loss from the pipe surface is 0.95 kw per meter of length, the external convective heat transfer coefficient (h) is: (a) 12.5 w/m"k (b) 18.6 w/mk (c) 23.7 w/mk (d) 27.9 w/mk (e) 33.5 w/mk

Find the kinematic pressure of 160kpa. for air, r-287 j/ kg k. and hair al viscosity of air at a temperature of 50°c and an absolute (10 points) (b) find the dynamic viscosity of air at 110 °c. sutherland constant for air is 111k