1.  The lens equation says that if an object is placed at a distance p from a lens, and an image is formed at a distance q from the lens, then the focal length f satisfies the equation 1/f = 1/p + 1/q. Assume that p = 2.3 ± 0.2 cm and q = 3.1 ± 0.2 cm.

a.  Estimate f, and find the uncertainty in the estimate.

b.  Which would provide a greater reduction in the uncertainty in f: reducing the uncertainty in p to 0.1 cm or reducing the uncertainty in q to 0.1 cm?

2.    The pressure P, temperature T, and volume V of one mole of an ideal gas are related by the equation PV = 8.31 T, when P is measured in kilopascals, T is measured in kelvins, and V is measured in liters.

a.   Assume that P = 242.52 ± 0.03 kPa and V = 10.103 ± 0.002 L. Estimate T, and find the uncertainty in the estimate.

b.  Assume that P = 242.52 ± 0.03 kPa and T = 290.11 ± 0.02 K. Estimate V, and find the uncertainty in the estimate.

c.    Assume that V = 10.103 ± 0.002 L and T = 290.11 ± 0.02 K. Estimate P, and find the uncertainty in the estimate.